TSTP Solution File: GEO284+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO284+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 05:16:37 EDT 2024
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 278
% Syntax : Number of formulae : 1196 ( 179 unt; 0 def)
% Number of atoms : 6584 (1950 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 9437 (4049 ~;3805 |;1237 &)
% ( 183 <=>; 163 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 190 ( 188 usr; 174 prp; 0-4 aty)
% Number of functors : 54 ( 54 usr; 16 con; 0-4 aty)
% Number of variables : 3872 (3515 !; 357 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2718,plain,
$false,
inference(avatar_sat_refutation,[],[f1585,f1590,f1595,f1600,f1605,f1614,f1623,f1628,f1633,f1638,f1645,f1650,f1655,f1660,f1664,f1668,f1672,f1676,f1680,f1684,f1688,f1692,f1696,f1700,f1704,f1708,f1712,f1716,f1720,f1724,f1728,f1732,f1736,f1740,f1745,f1764,f1768,f1772,f1776,f1780,f1784,f1788,f1792,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1830,f1838,f1842,f1846,f1850,f1854,f1858,f1862,f1867,f1871,f1875,f1896,f1900,f1905,f1909,f1913,f1917,f1921,f1925,f1929,f1933,f1937,f1941,f1945,f1949,f1953,f1957,f1961,f1965,f1969,f1973,f2056,f2060,f2064,f2068,f2072,f2076,f2080,f2084,f2088,f2092,f2096,f2100,f2104,f2108,f2112,f2116,f2120,f2124,f2128,f2132,f2136,f2140,f2144,f2148,f2152,f2156,f2160,f2169,f2181,f2189,f2193,f2197,f2201,f2205,f2209,f2213,f2217,f2226,f2244,f2248,f2252,f2262,f2266,f2270,f2274,f2278,f2357,f2372,f2376,f2394,f2398,f2416,f2420,f2424,f2428,f2432,f2436,f2440,f2444,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2582,f2588,f2592,f2596,f2600,f2604,f2608,f2612,f2616,f2620,f2626,f2671,f2676,f2680,f2684,f2688,f2692,f2696,f2700,f2704,f2708,f2717]) ).
fof(f2717,plain,
( spl52_11
| ~ spl52_4
| ~ spl52_5
| ~ spl52_70
| spl52_161 ),
inference(avatar_split_clause,[],[f2672,f2623,f1911,f1602,f1597,f1630]) ).
fof(f1630,plain,
( spl52_11
<=> vd1126 = vd1124 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_11])]) ).
fof(f1597,plain,
( spl52_4
<=> rpoint(vd1126) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_4])]) ).
fof(f1602,plain,
( spl52_5
<=> rpoint(vd1124) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_5])]) ).
fof(f1911,plain,
( spl52_70
<=> ! [X4,X3] :
( rline(sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_70])]) ).
fof(f2623,plain,
( spl52_161
<=> rline(sK10(vd1124,vd1126)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_161])]) ).
fof(f2672,plain,
( ~ rpoint(vd1124)
| ~ rpoint(vd1126)
| vd1126 = vd1124
| ~ spl52_70
| spl52_161 ),
inference(resolution,[],[f2625,f1912]) ).
fof(f1912,plain,
( ! [X3,X4] :
( rline(sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 )
| ~ spl52_70 ),
inference(avatar_component_clause,[],[f1911]) ).
fof(f2625,plain,
( ~ rline(sK10(vd1124,vd1126))
| spl52_161 ),
inference(avatar_component_clause,[],[f2623]) ).
fof(f2708,plain,
spl52_171,
inference(avatar_split_clause,[],[f1298,f2706]) ).
fof(f2706,plain,
( spl52_171
<=> ! [X5,X7,X6,X3] :
( rintersect(X3,X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X3)
| rS(X6,X7,X3)
| ~ rline(X5)
| ~ ron(X6,X5)
| ~ ron(X7,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_171])]) ).
fof(f1298,plain,
! [X3,X6,X7,X5] :
( rintersect(X3,X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X3)
| rS(X6,X7,X3)
| ~ rline(X5)
| ~ ron(X6,X5)
| ~ ron(X7,X5) ),
inference(equality_resolution,[],[f1297]) ).
fof(f1297,plain,
! [X2,X3,X6,X7,X5] :
( rintersect(X2,X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X3)
| rS(X6,X7,X2)
| ~ rline(X5)
| ~ ron(X6,X5)
| ~ ron(X7,X5)
| X2 != X3 ),
inference(equality_resolution,[],[f1296]) ).
fof(f1296,plain,
! [X2,X3,X6,X7,X4,X5] :
( rintersect(X2,X4)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X3)
| rS(X6,X7,X2)
| ~ rline(X5)
| ~ ron(X6,X4)
| ~ ron(X7,X4)
| X4 != X5
| X2 != X3 ),
inference(equality_resolution,[],[f1295]) ).
fof(f1295,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( rintersect(X2,X4)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X1 != X7
| ~ rline(X3)
| rS(X6,X1,X2)
| ~ rline(X5)
| ~ ron(X6,X4)
| ~ ron(X1,X4)
| X4 != X5
| X2 != X3 ),
inference(equality_resolution,[],[f808]) ).
fof(f808,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( rintersect(X2,X4)
| ~ rpoint(X6)
| X0 != X6
| ~ rpoint(X7)
| X1 != X7
| ~ rline(X3)
| rS(X0,X1,X2)
| ~ rline(X5)
| ~ ron(X0,X4)
| ~ ron(X1,X4)
| X4 != X5
| X2 != X3 ),
inference(cnf_transformation,[],[f422]) ).
fof(f422,plain,
! [X0,X1,X2,X3,X4,X5] :
( rintersect(X2,X4)
| ! [X6] :
( ~ rpoint(X6)
| X0 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X1 != X7 )
| ~ rline(X3)
| rS(X0,X1,X2)
| ~ rline(X5)
| ~ ron(X0,X4)
| ~ ron(X1,X4)
| X4 != X5
| X2 != X3 ),
inference(flattening,[],[f421]) ).
fof(f421,plain,
! [X0,X1,X2,X3,X4,X5] :
( rintersect(X2,X4)
| ! [X6] :
( ~ rpoint(X6)
| X0 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X1 != X7 )
| ~ rline(X3)
| rS(X0,X1,X2)
| ~ rline(X5)
| ~ ron(X0,X4)
| ~ ron(X1,X4)
| X4 != X5
| X2 != X3 ),
inference(ennf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ? [X6] :
( rpoint(X6)
& X0 = X6 )
& ? [X7] :
( rpoint(X7)
& X1 = X7 )
& rline(X3)
& ~ rS(X0,X1,X2)
& rline(X5)
& ron(X0,X4)
& ron(X1,X4)
& X4 = X5
& X2 = X3 )
=> rintersect(X2,X4) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X224,X225,X226,X227,X228,X229] :
( ( ? [X231] :
( rpoint(X231)
& X224 = X231 )
& ? [X230] :
( rpoint(X230)
& X225 = X230 )
& rline(X227)
& ~ rS(X224,X225,X226)
& rline(X229)
& ron(X224,X228)
& ron(X225,X228)
& X228 = X229
& X226 = X227 )
=> rintersect(X226,X228) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(127), 0), imp(cond(axiom(127), 0)))') ).
fof(f2704,plain,
spl52_170,
inference(avatar_split_clause,[],[f1226,f2702]) ).
fof(f2702,plain,
( spl52_170
<=> ! [X5,X4,X7,X6] :
( ~ ron(X6,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rcircle(X4)
| ~ ron(X5,X4)
| rinside(X7,X4)
| ~ rR(X7,X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_170])]) ).
fof(f1226,plain,
! [X6,X7,X4,X5] :
( ~ ron(X6,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rcircle(X4)
| ~ ron(X5,X4)
| rinside(X7,X4)
| ~ rR(X7,X5,X6) ),
inference(equality_resolution,[],[f1225]) ).
fof(f1225,plain,
! [X3,X6,X7,X4,X5] :
( ~ ron(X6,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rcircle(X4)
| X3 != X4
| ~ ron(X5,X3)
| rinside(X7,X3)
| ~ rR(X7,X5,X6) ),
inference(equality_resolution,[],[f1224]) ).
fof(f1224,plain,
! [X2,X3,X6,X7,X4,X5] :
( ~ ron(X6,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X2 != X7
| ~ rcircle(X4)
| X3 != X4
| ~ ron(X5,X3)
| rinside(X2,X3)
| ~ rR(X2,X5,X6) ),
inference(equality_resolution,[],[f1223]) ).
fof(f1223,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ ron(X1,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rcircle(X4)
| X3 != X4
| ~ ron(X5,X3)
| rinside(X2,X3)
| ~ rR(X2,X5,X1) ),
inference(equality_resolution,[],[f793]) ).
fof(f793,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ ron(X1,X3)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rcircle(X4)
| X3 != X4
| ~ ron(X0,X3)
| rinside(X2,X3)
| ~ rR(X2,X0,X1) ),
inference(cnf_transformation,[],[f406]) ).
fof(f406,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ ron(X1,X3)
& ~ ron(X1,X3) )
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rcircle(X4)
| X3 != X4
| ( ~ rinside(X0,X3)
& ~ ron(X0,X3) )
| rinside(X2,X3)
| ~ rR(X2,X0,X1) ),
inference(flattening,[],[f405]) ).
fof(f405,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ ron(X1,X3)
& ~ ron(X1,X3) )
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rcircle(X4)
| X3 != X4
| ( ~ rinside(X0,X3)
& ~ ron(X0,X3) )
| rinside(X2,X3)
| ~ rR(X2,X0,X1) ),
inference(ennf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& rcircle(X4)
& X3 = X4
& ( rinside(X0,X3)
| ron(X0,X3) )
& ~ rinside(X2,X3)
& rR(X2,X0,X1) )
=> ( ~ ron(X1,X3)
& ~ ron(X1,X3) ) ),
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X244,X245,X246,X247,X248] :
( ( ? [X251] :
( rpoint(X251)
& X244 = X251 )
& ? [X250] :
( rpoint(X250)
& X245 = X250 )
& ? [X249] :
( rpoint(X249)
& X246 = X249 )
& rcircle(X248)
& X247 = X248
& ( rinside(X244,X247)
| ron(X244,X247) )
& ~ rinside(X246,X247)
& rR(X246,X244,X245) )
=> ( ~ ron(X245,X247)
& ~ ron(X245,X247) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(123), 0), imp(cond(axiom(123), 0)))') ).
fof(f2700,plain,
spl52_169,
inference(avatar_split_clause,[],[f1222,f2698]) ).
fof(f2698,plain,
( spl52_169
<=> ! [X5,X4,X7,X6] :
( ~ ron(X6,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rcircle(X4)
| ~ rinside(X5,X4)
| rinside(X7,X4)
| ~ rR(X7,X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_169])]) ).
fof(f1222,plain,
! [X6,X7,X4,X5] :
( ~ ron(X6,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rcircle(X4)
| ~ rinside(X5,X4)
| rinside(X7,X4)
| ~ rR(X7,X5,X6) ),
inference(equality_resolution,[],[f1221]) ).
fof(f1221,plain,
! [X3,X6,X7,X4,X5] :
( ~ ron(X6,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rcircle(X4)
| X3 != X4
| ~ rinside(X5,X3)
| rinside(X7,X3)
| ~ rR(X7,X5,X6) ),
inference(equality_resolution,[],[f1220]) ).
fof(f1220,plain,
! [X2,X3,X6,X7,X4,X5] :
( ~ ron(X6,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X2 != X7
| ~ rcircle(X4)
| X3 != X4
| ~ rinside(X5,X3)
| rinside(X2,X3)
| ~ rR(X2,X5,X6) ),
inference(equality_resolution,[],[f1219]) ).
fof(f1219,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ ron(X1,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rcircle(X4)
| X3 != X4
| ~ rinside(X5,X3)
| rinside(X2,X3)
| ~ rR(X2,X5,X1) ),
inference(equality_resolution,[],[f794]) ).
fof(f794,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ ron(X1,X3)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rcircle(X4)
| X3 != X4
| ~ rinside(X0,X3)
| rinside(X2,X3)
| ~ rR(X2,X0,X1) ),
inference(cnf_transformation,[],[f406]) ).
fof(f2696,plain,
spl52_168,
inference(avatar_split_clause,[],[f1181,f2694]) ).
fof(f2694,plain,
( spl52_168
<=> ! [X5,X4,X7,X6] :
( ron(X6,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ ron(X5,X4)
| ~ ron(X7,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_168])]) ).
fof(f1181,plain,
! [X6,X7,X4,X5] :
( ron(X6,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ ron(X5,X4)
| ~ ron(X7,X4) ),
inference(equality_resolution,[],[f1180]) ).
fof(f1180,plain,
! [X3,X6,X7,X4,X5] :
( ron(X6,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ ron(X5,X3)
| ~ ron(X7,X3)
| X3 != X4 ),
inference(equality_resolution,[],[f1179]) ).
fof(f1179,plain,
! [X2,X3,X6,X7,X4,X5] :
( ron(X6,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| ~ rR(X6,X5,X2)
| ~ ron(X5,X3)
| ~ ron(X2,X3)
| X3 != X4 ),
inference(equality_resolution,[],[f1178]) ).
fof(f1178,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ron(X1,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| ~ rR(X1,X5,X2)
| ~ ron(X5,X3)
| ~ ron(X2,X3)
| X3 != X4 ),
inference(equality_resolution,[],[f781]) ).
fof(f781,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ron(X1,X3)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| ~ rR(X1,X0,X2)
| ~ ron(X0,X3)
| ~ ron(X2,X3)
| X3 != X4 ),
inference(cnf_transformation,[],[f394]) ).
fof(f394,plain,
! [X0,X1,X2,X3,X4] :
( ron(X1,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| ~ rR(X1,X0,X2)
| ~ ron(X0,X3)
| ~ ron(X2,X3)
| X3 != X4 ),
inference(flattening,[],[f393]) ).
fof(f393,plain,
! [X0,X1,X2,X3,X4] :
( ron(X1,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| ~ rR(X1,X0,X2)
| ~ ron(X0,X3)
| ~ ron(X2,X3)
| X3 != X4 ),
inference(ennf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& rline(X4)
& rR(X1,X0,X2)
& ron(X0,X3)
& ron(X2,X3)
& X3 = X4 )
=> ron(X1,X3) ),
inference(rectify,[],[f89]) ).
fof(f89,axiom,
! [X405,X406,X407,X408,X409] :
( ( ? [X412] :
( rpoint(X412)
& X405 = X412 )
& ? [X411] :
( rpoint(X411)
& X406 = X411 )
& ? [X410] :
( rpoint(X410)
& X407 = X410 )
& rline(X409)
& rR(X406,X405,X407)
& ron(X405,X408)
& ron(X407,X408)
& X408 = X409 )
=> ron(X406,X408) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(85), 0), imp(cond(axiom(85), 0)))') ).
fof(f2692,plain,
spl52_167,
inference(avatar_split_clause,[],[f1177,f2690]) ).
fof(f2690,plain,
( spl52_167
<=> ! [X5,X4,X7,X6] :
( ron(X7,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ ron(X5,X4)
| ~ ron(X6,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_167])]) ).
fof(f1177,plain,
! [X6,X7,X4,X5] :
( ron(X7,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ ron(X5,X4)
| ~ ron(X6,X4) ),
inference(equality_resolution,[],[f1176]) ).
fof(f1176,plain,
! [X3,X6,X7,X4,X5] :
( ron(X7,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ ron(X5,X3)
| ~ ron(X6,X3)
| X3 != X4 ),
inference(equality_resolution,[],[f1175]) ).
fof(f1175,plain,
! [X2,X3,X6,X7,X4,X5] :
( ron(X2,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| ~ rR(X6,X5,X2)
| ~ ron(X5,X3)
| ~ ron(X6,X3)
| X3 != X4 ),
inference(equality_resolution,[],[f1174]) ).
fof(f1174,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ron(X2,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| ~ rR(X1,X5,X2)
| ~ ron(X5,X3)
| ~ ron(X1,X3)
| X3 != X4 ),
inference(equality_resolution,[],[f780]) ).
fof(f780,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ron(X2,X3)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| ~ rR(X1,X0,X2)
| ~ ron(X0,X3)
| ~ ron(X1,X3)
| X3 != X4 ),
inference(cnf_transformation,[],[f392]) ).
fof(f392,plain,
! [X0,X1,X2,X3,X4] :
( ron(X2,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| ~ rR(X1,X0,X2)
| ~ ron(X0,X3)
| ~ ron(X1,X3)
| X3 != X4 ),
inference(flattening,[],[f391]) ).
fof(f391,plain,
! [X0,X1,X2,X3,X4] :
( ron(X2,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| ~ rR(X1,X0,X2)
| ~ ron(X0,X3)
| ~ ron(X1,X3)
| X3 != X4 ),
inference(ennf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& rline(X4)
& rR(X1,X0,X2)
& ron(X0,X3)
& ron(X1,X3)
& X3 = X4 )
=> ron(X2,X3) ),
inference(rectify,[],[f90]) ).
fof(f90,axiom,
! [X413,X414,X415,X416,X417] :
( ( ? [X420] :
( rpoint(X420)
& X413 = X420 )
& ? [X419] :
( rpoint(X419)
& X414 = X419 )
& ? [X418] :
( rpoint(X418)
& X415 = X418 )
& rline(X417)
& rR(X414,X413,X415)
& ron(X413,X416)
& ron(X414,X416)
& X416 = X417 )
=> ron(X415,X416) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))') ).
fof(f2688,plain,
spl52_166,
inference(avatar_split_clause,[],[f1034,f2686]) ).
fof(f2686,plain,
( spl52_166
<=> ! [X6,X5,X1] :
( rR(sK23(X5,X6),X5,X6)
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1)
| X5 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_166])]) ).
fof(f1034,plain,
! [X1,X6,X5] :
( rR(sK23(X5,X6),X5,X6)
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1)
| X5 = X6 ),
inference(equality_resolution,[],[f1033]) ).
fof(f1033,plain,
! [X3,X1,X6,X5] :
( rR(sK23(X5,X3),X5,X3)
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X5,X1)
| ~ ron(X3,X1)
| X3 = X5 ),
inference(equality_resolution,[],[f1032]) ).
fof(f1032,plain,
! [X2,X3,X1,X6,X5] :
( rR(sK23(X2,X3),X2,X3)
| ~ rline(X1)
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X1)
| ~ ron(X3,X1)
| X2 = X3 ),
inference(equality_resolution,[],[f712]) ).
fof(f712,plain,
! [X2,X3,X0,X1,X6,X5] :
( rR(sK23(X2,X3),X2,X3)
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(cnf_transformation,[],[f531]) ).
fof(f531,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK23(X2,X3))
& rR(sK23(X2,X3),X2,X3) )
| ~ rline(X1)
| X0 != X1
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X3 != X6 )
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f529,f530]) ).
fof(f530,plain,
! [X2,X3] :
( ? [X4] :
( rpoint(X4)
& rR(X4,X2,X3) )
=> ( rpoint(sK23(X2,X3))
& rR(sK23(X2,X3),X2,X3) ) ),
introduced(choice_axiom,[]) ).
fof(f529,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& rR(X4,X2,X3) )
| ~ rline(X1)
| X0 != X1
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X3 != X6 )
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(rectify,[],[f326]) ).
fof(f326,plain,
! [X0,X1,X2,X3] :
( ? [X6] :
( rpoint(X6)
& rR(X6,X2,X3) )
| ~ rline(X1)
| X0 != X1
| ! [X4] :
( ~ rpoint(X4)
| X2 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X3 != X5 )
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(flattening,[],[f325]) ).
fof(f325,plain,
! [X0,X1,X2,X3] :
( ? [X6] :
( rpoint(X6)
& rR(X6,X2,X3) )
| ~ rline(X1)
| X0 != X1
| ! [X4] :
( ~ rpoint(X4)
| X2 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X3 != X5 )
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(ennf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& ? [X4] :
( rpoint(X4)
& X2 = X4 )
& ? [X5] :
( rpoint(X5)
& X3 = X5 )
& ron(X2,X0)
& ron(X3,X0)
& X2 != X3 )
=> ? [X6] :
( rpoint(X6)
& rR(X6,X2,X3) ) ),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X540,X541,X542,X543] :
( ( rline(X541)
& X540 = X541
& ? [X545] :
( rpoint(X545)
& X542 = X545 )
& ? [X544] :
( rpoint(X544)
& X543 = X544 )
& ron(X542,X540)
& ron(X543,X540)
& X542 != X543 )
=> ? [X546] :
( rpoint(X546)
& rR(X546,X542,X543) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(23), 0), imp(cond(axiom(23), 0)))') ).
fof(f2684,plain,
spl52_165,
inference(avatar_split_clause,[],[f1028,f2682]) ).
fof(f2682,plain,
( spl52_165
<=> ! [X6,X5,X1] :
( rR(X6,X5,sK22(X5,X6))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1)
| X5 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_165])]) ).
fof(f1028,plain,
! [X1,X6,X5] :
( rR(X6,X5,sK22(X5,X6))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1)
| X5 = X6 ),
inference(equality_resolution,[],[f1027]) ).
fof(f1027,plain,
! [X3,X1,X6,X5] :
( rR(X3,X5,sK22(X5,X3))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X5,X1)
| ~ ron(X3,X1)
| X3 = X5 ),
inference(equality_resolution,[],[f1026]) ).
fof(f1026,plain,
! [X2,X3,X1,X6,X5] :
( rR(X3,X2,sK22(X2,X3))
| ~ rline(X1)
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X1)
| ~ ron(X3,X1)
| X2 = X3 ),
inference(equality_resolution,[],[f710]) ).
fof(f710,plain,
! [X2,X3,X0,X1,X6,X5] :
( rR(X3,X2,sK22(X2,X3))
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(cnf_transformation,[],[f528]) ).
fof(f528,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK22(X2,X3))
& rR(X3,X2,sK22(X2,X3)) )
| ~ rline(X1)
| X0 != X1
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X3 != X6 )
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f526,f527]) ).
fof(f527,plain,
! [X2,X3] :
( ? [X4] :
( rpoint(X4)
& rR(X3,X2,X4) )
=> ( rpoint(sK22(X2,X3))
& rR(X3,X2,sK22(X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f526,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& rR(X3,X2,X4) )
| ~ rline(X1)
| X0 != X1
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X3 != X6 )
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(rectify,[],[f324]) ).
fof(f324,plain,
! [X0,X1,X2,X3] :
( ? [X6] :
( rpoint(X6)
& rR(X3,X2,X6) )
| ~ rline(X1)
| X0 != X1
| ! [X4] :
( ~ rpoint(X4)
| X2 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X3 != X5 )
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(flattening,[],[f323]) ).
fof(f323,plain,
! [X0,X1,X2,X3] :
( ? [X6] :
( rpoint(X6)
& rR(X3,X2,X6) )
| ~ rline(X1)
| X0 != X1
| ! [X4] :
( ~ rpoint(X4)
| X2 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X3 != X5 )
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(ennf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& ? [X4] :
( rpoint(X4)
& X2 = X4 )
& ? [X5] :
( rpoint(X5)
& X3 = X5 )
& ron(X2,X0)
& ron(X3,X0)
& X2 != X3 )
=> ? [X6] :
( rpoint(X6)
& rR(X3,X2,X6) ) ),
inference(rectify,[],[f105]) ).
fof(f105,axiom,
! [X513,X514,X515,X516] :
( ( rline(X514)
& X513 = X514
& ? [X518] :
( rpoint(X518)
& X515 = X518 )
& ? [X517] :
( rpoint(X517)
& X516 = X517 )
& ron(X515,X513)
& ron(X516,X513)
& X515 != X516 )
=> ? [X519] :
( rpoint(X519)
& rR(X516,X515,X519) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(29), 0), imp(cond(axiom(29), 0)))') ).
fof(f2680,plain,
spl52_164,
inference(avatar_split_clause,[],[f984,f2678]) ).
fof(f2678,plain,
( spl52_164
<=> ! [X4,X5,X3] :
( vf(X3,X5) = vplus(vf(X3,X4),vf(X4,X5))
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_164])]) ).
fof(f984,plain,
! [X3,X4,X5] :
( vf(X3,X5) = vplus(vf(X3,X4),vf(X4,X5))
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X3,X5) ),
inference(equality_resolution,[],[f983]) ).
fof(f983,plain,
! [X2,X3,X4,X5] :
( vf(X3,X2) = vplus(vf(X3,X4),vf(X4,X2))
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X4,X3,X2) ),
inference(equality_resolution,[],[f982]) ).
fof(f982,plain,
! [X2,X3,X1,X4,X5] :
( vf(X3,X2) = vplus(vf(X3,X1),vf(X1,X2))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X3,X2) ),
inference(equality_resolution,[],[f697]) ).
fof(f697,plain,
! [X2,X3,X0,X1,X4,X5] :
( vplus(vf(X0,X1),vf(X1,X2)) = vf(X0,X2)
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X0,X2) ),
inference(cnf_transformation,[],[f314]) ).
fof(f314,plain,
! [X0,X1,X2] :
( vplus(vf(X0,X1),vf(X1,X2)) = vf(X0,X2)
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ~ rR(X1,X0,X2) ),
inference(flattening,[],[f313]) ).
fof(f313,plain,
! [X0,X1,X2] :
( vplus(vf(X0,X1),vf(X1,X2)) = vf(X0,X2)
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ~ rR(X1,X0,X2) ),
inference(ennf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rR(X1,X0,X2) )
=> vplus(vf(X0,X1),vf(X1,X2)) = vf(X0,X2) ),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X156,X157,X158] :
( ( ? [X161] :
( rpoint(X161)
& X156 = X161 )
& ? [X160] :
( rpoint(X160)
& X157 = X160 )
& ? [X159] :
( rpoint(X159)
& X158 = X159 )
& rR(X157,X156,X158) )
=> vplus(vf(X156,X157),vf(X157,X158)) = vf(X156,X158) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))') ).
fof(f2676,plain,
spl52_163,
inference(avatar_split_clause,[],[f981,f2674]) ).
fof(f2674,plain,
( spl52_163
<=> ! [X4,X5,X3] :
( vangle(X3,X4,X5) = vangle(X5,X4,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X3 = X4
| X3 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_163])]) ).
fof(f981,plain,
! [X3,X4,X5] :
( vangle(X3,X4,X5) = vangle(X5,X4,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X3 = X4
| X3 = X5 ),
inference(equality_resolution,[],[f980]) ).
fof(f980,plain,
! [X2,X3,X4,X5] :
( vangle(X3,X4,X2) = vangle(X2,X4,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X2 != X5
| X3 = X4
| X2 = X3 ),
inference(equality_resolution,[],[f979]) ).
fof(f979,plain,
! [X2,X3,X1,X4,X5] :
( vangle(X3,X1,X2) = vangle(X2,X1,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| X1 = X3
| X2 = X3 ),
inference(equality_resolution,[],[f696]) ).
fof(f696,plain,
! [X2,X3,X0,X1,X4,X5] :
( vangle(X0,X1,X2) = vangle(X2,X1,X0)
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| X0 = X1
| X0 = X2 ),
inference(cnf_transformation,[],[f312]) ).
fof(f312,plain,
! [X0,X1,X2] :
( vangle(X0,X1,X2) = vangle(X2,X1,X0)
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| X0 = X1
| X0 = X2 ),
inference(flattening,[],[f311]) ).
fof(f311,plain,
! [X0,X1,X2] :
( vangle(X0,X1,X2) = vangle(X2,X1,X0)
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| X0 = X1
| X0 = X2 ),
inference(ennf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& X0 != X1
& X0 != X2 )
=> vangle(X0,X1,X2) = vangle(X2,X1,X0) ),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X728,X729,X730] :
( ( ? [X733] :
( rpoint(X733)
& X728 = X733 )
& ? [X732] :
( rpoint(X732)
& X729 = X732 )
& ? [X731] :
( rpoint(X731)
& X730 = X731 )
& X728 != X729
& X728 != X730 )
=> vangle(X728,X729,X730) = vangle(X730,X729,X728) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(168), 0), imp(cond(axiom(168), 0)))') ).
fof(f2671,plain,
spl52_162,
inference(avatar_split_clause,[],[f929,f2669]) ).
fof(f2669,plain,
( spl52_162
<=> ! [X4,X5,X3] :
( rpoint(vskolem1078(X3,X3,X4,X5))
| ~ rpoint(X3)
| X3 = X4
| X3 = X5
| ~ rpoint(X4)
| ~ rpoint(X5)
| X4 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_162])]) ).
fof(f929,plain,
! [X3,X4,X5] :
( rpoint(vskolem1078(X3,X3,X4,X5))
| ~ rpoint(X3)
| X3 = X4
| X3 = X5
| ~ rpoint(X4)
| ~ rpoint(X5)
| X4 = X5 ),
inference(equality_resolution,[],[f928]) ).
fof(f928,plain,
! [X3,X1,X4,X5] :
( rpoint(vskolem1078(X3,X3,X4,X1))
| ~ rpoint(X3)
| X3 = X4
| X1 = X3
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| X1 = X4 ),
inference(equality_resolution,[],[f927]) ).
fof(f927,plain,
! [X3,X0,X1,X4,X5] :
( rpoint(vskolem1078(X3,X3,X0,X1))
| ~ rpoint(X3)
| X0 = X3
| X1 = X3
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| X0 = X1 ),
inference(equality_resolution,[],[f658]) ).
fof(f658,plain,
! [X2,X3,X0,X1,X4,X5] :
( rpoint(vskolem1078(X2,X3,X0,X1))
| ~ rpoint(X3)
| X0 = X2
| X1 = X2
| X2 != X3
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| X0 = X1 ),
inference(cnf_transformation,[],[f491]) ).
fof(f491,plain,
! [X0,X1] :
( ! [X2,X3] :
( rpoint(vskolem1078(X2,X3,X0,X1))
| ~ rpoint(X3)
| X0 = X2
| X1 = X2
| X2 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| X0 = X1 ),
inference(rectify,[],[f278]) ).
fof(f278,plain,
! [X0,X1] :
( ! [X4,X5] :
( rpoint(vskolem1078(X4,X5,X0,X1))
| ~ rpoint(X5)
| X0 = X4
| X1 = X4
| X4 != X5 )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 )
| X0 = X1 ),
inference(flattening,[],[f277]) ).
fof(f277,plain,
! [X0,X1] :
( ! [X4,X5] :
( rpoint(vskolem1078(X4,X5,X0,X1))
| ~ rpoint(X5)
| X0 = X4
| X1 = X4
| X4 != X5 )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 )
| X0 = X1 ),
inference(ennf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( ( ? [X2] :
( rpoint(X2)
& X0 = X2 )
& ? [X3] :
( rpoint(X3)
& X1 = X3 )
& X0 != X1 )
=> ! [X4,X5] :
( ( rpoint(X5)
& X0 != X4
& X1 != X4
& X4 = X5 )
=> rpoint(vskolem1078(X4,X5,X0,X1)) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X88,X89] :
( ( ? [X91] :
( rpoint(X91)
& X88 = X91 )
& ? [X90] :
( rpoint(X90)
& X89 = X90 )
& X88 != X89 )
=> ! [X92,X93] :
( ( rpoint(X93)
& X88 != X92
& X89 != X92
& X92 = X93 )
=> rpoint(vskolem1078(X92,X93,X88,X89)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(219), 0), 1)') ).
fof(f2626,plain,
( ~ spl52_5
| spl52_11
| ~ spl52_161
| ~ spl52_4
| ~ spl52_96
| ~ spl52_147 ),
inference(avatar_split_clause,[],[f2584,f2494,f2094,f1597,f2623,f1630,f1602]) ).
fof(f2094,plain,
( spl52_96
<=> ! [X4,X3] :
( ron(X4,sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_96])]) ).
fof(f2494,plain,
( spl52_147
<=> ! [X0] :
( ~ rpoint(X0)
| ~ ron(vd1126,sK10(vd1124,X0))
| ~ rline(sK10(vd1124,X0))
| vd1124 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_147])]) ).
fof(f2584,plain,
( ~ rpoint(vd1126)
| ~ rline(sK10(vd1124,vd1126))
| vd1126 = vd1124
| ~ rpoint(vd1124)
| ~ spl52_96
| ~ spl52_147 ),
inference(duplicate_literal_removal,[],[f2583]) ).
fof(f2583,plain,
( ~ rpoint(vd1126)
| ~ rline(sK10(vd1124,vd1126))
| vd1126 = vd1124
| ~ rpoint(vd1124)
| ~ rpoint(vd1126)
| vd1126 = vd1124
| ~ spl52_96
| ~ spl52_147 ),
inference(resolution,[],[f2495,f2095]) ).
fof(f2095,plain,
( ! [X3,X4] :
( ron(X4,sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 )
| ~ spl52_96 ),
inference(avatar_component_clause,[],[f2094]) ).
fof(f2495,plain,
( ! [X0] :
( ~ ron(vd1126,sK10(vd1124,X0))
| ~ rpoint(X0)
| ~ rline(sK10(vd1124,X0))
| vd1124 = X0 )
| ~ spl52_147 ),
inference(avatar_component_clause,[],[f2494]) ).
fof(f2620,plain,
spl52_160,
inference(avatar_split_clause,[],[f1332,f2618]) ).
fof(f2618,plain,
( spl52_160
<=> ! [X3,X5,X2,X1] :
( ron(X1,X3)
| vf(X2,X1) != vf(X2,X5)
| ~ rpoint(X1)
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| ~ ron(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_160])]) ).
fof(f1332,plain,
! [X2,X3,X1,X5] :
( ron(X1,X3)
| vf(X2,X1) != vf(X2,X5)
| ~ rpoint(X1)
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| ~ ron(X5,X3) ),
inference(equality_resolution,[],[f1331]) ).
fof(f1331,plain,
! [X2,X3,X1,X4,X5] :
( ron(X1,X3)
| vf(X2,X1) != vf(X2,X4)
| ~ rpoint(X1)
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X4,X3) ),
inference(equality_resolution,[],[f818]) ).
fof(f818,plain,
! [X2,X3,X0,X1,X4,X5] :
( ron(X0,X3)
| vf(X2,X0) != vf(X2,X4)
| ~ rpoint(X1)
| X0 != X1
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X4,X3) ),
inference(cnf_transformation,[],[f580]) ).
fof(f580,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( vf(X2,X0) = vf(X2,X4)
| ~ ron(X0,X3) )
& ( ron(X0,X3)
| vf(X2,X0) != vf(X2,X4) ) )
| ~ rpoint(X1)
| X0 != X1
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X4,X3) ),
inference(nnf_transformation,[],[f432]) ).
fof(f432,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vf(X2,X0) = vf(X2,X4)
<=> ron(X0,X3) )
| ~ rpoint(X1)
| X0 != X1
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X4,X3) ),
inference(flattening,[],[f431]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vf(X2,X0) = vf(X2,X4)
<=> ron(X0,X3) )
| ~ rpoint(X1)
| X0 != X1
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X4,X3) ),
inference(ennf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rpoint(X1)
& X0 = X1
& rcenter(X2,X3)
& rpoint(X5)
& X4 = X5
& ron(X4,X3) )
=> ( vf(X2,X0) = vf(X2,X4)
<=> ron(X0,X3) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X8,X9,X10,X11,X12,X13] :
( ( rpoint(X9)
& X8 = X9
& rcenter(X10,X11)
& rpoint(X13)
& X12 = X13
& ron(X12,X11) )
=> ( vf(X10,X8) = vf(X10,X12)
<=> ron(X8,X11) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))') ).
fof(f2616,plain,
spl52_159,
inference(avatar_split_clause,[],[f1330,f2614]) ).
fof(f2614,plain,
( spl52_159
<=> ! [X3,X5,X2,X1] :
( vf(X2,X1) = vf(X2,X5)
| ~ ron(X1,X3)
| ~ rpoint(X1)
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| ~ ron(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_159])]) ).
fof(f1330,plain,
! [X2,X3,X1,X5] :
( vf(X2,X1) = vf(X2,X5)
| ~ ron(X1,X3)
| ~ rpoint(X1)
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| ~ ron(X5,X3) ),
inference(equality_resolution,[],[f1329]) ).
fof(f1329,plain,
! [X2,X3,X1,X4,X5] :
( vf(X2,X1) = vf(X2,X4)
| ~ ron(X1,X3)
| ~ rpoint(X1)
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X4,X3) ),
inference(equality_resolution,[],[f819]) ).
fof(f819,plain,
! [X2,X3,X0,X1,X4,X5] :
( vf(X2,X0) = vf(X2,X4)
| ~ ron(X0,X3)
| ~ rpoint(X1)
| X0 != X1
| ~ rcenter(X2,X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X4,X3) ),
inference(cnf_transformation,[],[f580]) ).
fof(f2612,plain,
spl52_158,
inference(avatar_split_clause,[],[f1304,f2610]) ).
fof(f2610,plain,
( spl52_158
<=> ! [X5,X1,X3] :
( rS(sK40(X1,X3,X5),X3,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1)
| ~ rpoint(X5)
| ~ rS(X5,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_158])]) ).
fof(f1304,plain,
! [X3,X1,X5] :
( rS(sK40(X1,X3,X5),X3,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1)
| ~ rpoint(X5)
| ~ rS(X5,X3,X1) ),
inference(equality_resolution,[],[f1303]) ).
fof(f1303,plain,
! [X2,X3,X1,X5] :
( rS(sK40(X1,X2,X5),X2,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| ~ rpoint(X5)
| ~ rS(X5,X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f1302]) ).
fof(f1302,plain,
! [X2,X3,X1,X4,X5] :
( rS(sK40(X1,X2,X4),X2,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| ~ rpoint(X5)
| ~ rS(X4,X2,X1)
| X4 != X5
| X2 != X3 ),
inference(equality_resolution,[],[f811]) ).
fof(f811,plain,
! [X2,X3,X0,X1,X4,X5] :
( rS(sK40(X0,X2,X4),X2,X0)
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| ~ rpoint(X5)
| ~ rS(X4,X2,X0)
| X4 != X5
| X2 != X3 ),
inference(cnf_transformation,[],[f576]) ).
fof(f576,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rpoint(sK40(X0,X2,X4))
& rS(sK40(X0,X2,X4),X2,X0)
& sK40(X0,X2,X4) != X2
& sK40(X0,X2,X4) != X4 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| ~ rpoint(X5)
| ~ rS(X4,X2,X0)
| X4 != X5
| X2 != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f424,f575]) ).
fof(f575,plain,
! [X0,X2,X4] :
( ? [X6] :
( rpoint(X6)
& rS(X6,X2,X0)
& X2 != X6
& X4 != X6 )
=> ( rpoint(sK40(X0,X2,X4))
& rS(sK40(X0,X2,X4),X2,X0)
& sK40(X0,X2,X4) != X2
& sK40(X0,X2,X4) != X4 ) ),
introduced(choice_axiom,[]) ).
fof(f424,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( rpoint(X6)
& rS(X6,X2,X0)
& X2 != X6
& X4 != X6 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| ~ rpoint(X5)
| ~ rS(X4,X2,X0)
| X4 != X5
| X2 != X3 ),
inference(flattening,[],[f423]) ).
fof(f423,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( rpoint(X6)
& rS(X6,X2,X0)
& X2 != X6
& X4 != X6 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| ~ rpoint(X5)
| ~ rS(X4,X2,X0)
| X4 != X5
| X2 != X3 ),
inference(ennf_transformation,[],[f212]) ).
fof(f212,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& ~ ron(X2,X0)
& rpoint(X5)
& rS(X4,X2,X0)
& X4 = X5
& X2 = X3 )
=> ? [X6] :
( rpoint(X6)
& rS(X6,X2,X0)
& X2 != X6
& X4 != X6 ) ),
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X492,X493,X494,X495,X496,X497] :
( ( rline(X493)
& X492 = X493
& rpoint(X495)
& ~ ron(X494,X492)
& rpoint(X497)
& rS(X496,X494,X492)
& X496 = X497
& X494 = X495 )
=> ? [X498] :
( rpoint(X498)
& rS(X498,X494,X492)
& X494 != X498
& X496 != X498 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(35), 0), imp(cond(axiom(35), 0)))') ).
fof(f2608,plain,
spl52_157,
inference(avatar_split_clause,[],[f1254,f2606]) ).
fof(f2606,plain,
( spl52_157
<=> ! [X5,X4,X7,X6] :
( rS(X6,X7,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rS(X5,X6,X4)
| ~ rS(X5,X7,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_157])]) ).
fof(f1254,plain,
! [X6,X7,X4,X5] :
( rS(X6,X7,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rS(X5,X6,X4)
| ~ rS(X5,X7,X4) ),
inference(equality_resolution,[],[f1253]) ).
fof(f1253,plain,
! [X3,X6,X7,X4,X5] :
( rS(X6,X7,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| X3 != X4
| ~ rS(X5,X6,X3)
| ~ rS(X5,X7,X3) ),
inference(equality_resolution,[],[f1252]) ).
fof(f1252,plain,
! [X2,X3,X6,X7,X4,X5] :
( rS(X6,X2,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rS(X5,X6,X3)
| ~ rS(X5,X2,X3) ),
inference(equality_resolution,[],[f1251]) ).
fof(f1251,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( rS(X1,X2,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rS(X5,X1,X3)
| ~ rS(X5,X2,X3) ),
inference(equality_resolution,[],[f799]) ).
fof(f799,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( rS(X1,X2,X3)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rS(X0,X1,X3)
| ~ rS(X0,X2,X3) ),
inference(cnf_transformation,[],[f412]) ).
fof(f412,plain,
! [X0,X1,X2,X3,X4] :
( rS(X1,X2,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| X3 != X4
| ~ rS(X0,X1,X3)
| ~ rS(X0,X2,X3) ),
inference(flattening,[],[f411]) ).
fof(f411,plain,
! [X0,X1,X2,X3,X4] :
( rS(X1,X2,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| X3 != X4
| ~ rS(X0,X1,X3)
| ~ rS(X0,X2,X3) ),
inference(ennf_transformation,[],[f205]) ).
fof(f205,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& rline(X4)
& X3 = X4
& rS(X0,X1,X3)
& rS(X0,X2,X3) )
=> rS(X1,X2,X3) ),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X357,X358,X359,X360,X361] :
( ( ? [X364] :
( rpoint(X364)
& X357 = X364 )
& ? [X363] :
( rpoint(X363)
& X358 = X363 )
& ? [X362] :
( rpoint(X362)
& X359 = X362 )
& rline(X361)
& X360 = X361
& rS(X357,X358,X360)
& rS(X357,X359,X360) )
=> rS(X358,X359,X360) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(101), 0), imp(cond(axiom(101), 0)))') ).
fof(f2604,plain,
spl52_156,
inference(avatar_split_clause,[],[f1250,f2602]) ).
fof(f2602,plain,
( spl52_156
<=> ! [X5,X4,X7,X6] :
( rS(X5,X6,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ rS(X5,X7,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_156])]) ).
fof(f1250,plain,
! [X6,X7,X4,X5] :
( rS(X5,X6,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ rS(X5,X7,X4) ),
inference(equality_resolution,[],[f1249]) ).
fof(f1249,plain,
! [X3,X6,X7,X4,X5] :
( rS(X5,X6,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| X3 != X4
| ~ rR(X6,X5,X7)
| ~ rS(X5,X7,X3) ),
inference(equality_resolution,[],[f1248]) ).
fof(f1248,plain,
! [X2,X3,X6,X7,X4,X5] :
( rS(X5,X6,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rR(X6,X5,X2)
| ~ rS(X5,X2,X3) ),
inference(equality_resolution,[],[f1247]) ).
fof(f1247,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( rS(X5,X1,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rR(X1,X5,X2)
| ~ rS(X5,X2,X3) ),
inference(equality_resolution,[],[f798]) ).
fof(f798,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( rS(X0,X1,X3)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rR(X1,X0,X2)
| ~ rS(X0,X2,X3) ),
inference(cnf_transformation,[],[f410]) ).
fof(f410,plain,
! [X0,X1,X2,X3,X4] :
( rS(X0,X1,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| X3 != X4
| ~ rR(X1,X0,X2)
| ~ rS(X0,X2,X3) ),
inference(flattening,[],[f409]) ).
fof(f409,plain,
! [X0,X1,X2,X3,X4] :
( rS(X0,X1,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| X3 != X4
| ~ rR(X1,X0,X2)
| ~ rS(X0,X2,X3) ),
inference(ennf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& rline(X4)
& X3 = X4
& rR(X1,X0,X2)
& rS(X0,X2,X3) )
=> rS(X0,X1,X3) ),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X341,X342,X343,X344,X345] :
( ( ? [X348] :
( rpoint(X348)
& X341 = X348 )
& ? [X347] :
( rpoint(X347)
& X342 = X347 )
& ? [X346] :
( rpoint(X346)
& X343 = X346 )
& rline(X345)
& X344 = X345
& rR(X342,X341,X343)
& rS(X341,X343,X344) )
=> rS(X341,X342,X344) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(105), 0), imp(cond(axiom(105), 0)))') ).
fof(f2600,plain,
spl52_155,
inference(avatar_split_clause,[],[f1139,f2598]) ).
fof(f2598,plain,
( spl52_155
<=> ! [X5,X4,X7,X6] :
( rR(X7,X4,X6)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rR(X5,X4,X6)
| ~ rR(X7,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_155])]) ).
fof(f1139,plain,
! [X6,X7,X4,X5] :
( rR(X7,X4,X6)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rR(X5,X4,X6)
| ~ rR(X7,X4,X5) ),
inference(equality_resolution,[],[f1138]) ).
fof(f1138,plain,
! [X3,X6,X7,X4,X5] :
( rR(X3,X4,X6)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X5,X4,X6)
| ~ rR(X3,X4,X5) ),
inference(equality_resolution,[],[f1137]) ).
fof(f1137,plain,
! [X2,X3,X6,X7,X4,X5] :
( rR(X3,X4,X2)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X5,X4,X2)
| ~ rR(X3,X4,X5) ),
inference(equality_resolution,[],[f1136]) ).
fof(f1136,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( rR(X3,X4,X2)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X1,X4,X2)
| ~ rR(X3,X4,X1) ),
inference(equality_resolution,[],[f765]) ).
fof(f765,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( rR(X3,X0,X2)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X1,X0,X2)
| ~ rR(X3,X0,X1) ),
inference(cnf_transformation,[],[f378]) ).
fof(f378,plain,
! [X0,X1,X2,X3] :
( rR(X3,X0,X2)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 )
| ~ rR(X1,X0,X2)
| ~ rR(X3,X0,X1) ),
inference(flattening,[],[f377]) ).
fof(f377,plain,
! [X0,X1,X2,X3] :
( rR(X3,X0,X2)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 )
| ~ rR(X1,X0,X2)
| ~ rR(X3,X0,X1) ),
inference(ennf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( rpoint(X4)
& X0 = X4 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& ? [X6] :
( rpoint(X6)
& X2 = X6 )
& ? [X7] :
( rpoint(X7)
& X3 = X7 )
& rR(X1,X0,X2)
& rR(X3,X0,X1) )
=> rR(X3,X0,X2) ),
inference(rectify,[],[f88]) ).
fof(f88,axiom,
! [X397,X398,X399,X400] :
( ( ? [X404] :
( rpoint(X404)
& X397 = X404 )
& ? [X403] :
( rpoint(X403)
& X398 = X403 )
& ? [X402] :
( rpoint(X402)
& X399 = X402 )
& ? [X401] :
( rpoint(X401)
& X400 = X401 )
& rR(X398,X397,X399)
& rR(X400,X397,X398) )
=> rR(X400,X397,X399) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(87), 0), imp(cond(axiom(87), 0)))') ).
fof(f2596,plain,
spl52_154,
inference(avatar_split_clause,[],[f1135,f2594]) ).
fof(f2594,plain,
( spl52_154
<=> ! [X5,X4,X7,X6] :
( rR(X5,X4,X7)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rR(X5,X4,X6)
| ~ rR(X6,X5,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_154])]) ).
fof(f1135,plain,
! [X6,X7,X4,X5] :
( rR(X5,X4,X7)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rR(X5,X4,X6)
| ~ rR(X6,X5,X7) ),
inference(equality_resolution,[],[f1134]) ).
fof(f1134,plain,
! [X3,X6,X7,X4,X5] :
( rR(X5,X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X5,X4,X6)
| ~ rR(X6,X5,X3) ),
inference(equality_resolution,[],[f1133]) ).
fof(f1133,plain,
! [X2,X3,X6,X7,X4,X5] :
( rR(X5,X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X5,X4,X2)
| ~ rR(X2,X5,X3) ),
inference(equality_resolution,[],[f1132]) ).
fof(f1132,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( rR(X1,X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X1,X4,X2)
| ~ rR(X2,X1,X3) ),
inference(equality_resolution,[],[f764]) ).
fof(f764,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( rR(X1,X0,X3)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X1,X0,X2)
| ~ rR(X2,X1,X3) ),
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
! [X0,X1,X2,X3] :
( rR(X1,X0,X3)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 )
| ~ rR(X1,X0,X2)
| ~ rR(X2,X1,X3) ),
inference(flattening,[],[f375]) ).
fof(f375,plain,
! [X0,X1,X2,X3] :
( rR(X1,X0,X3)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 )
| ~ rR(X1,X0,X2)
| ~ rR(X2,X1,X3) ),
inference(ennf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( rpoint(X4)
& X0 = X4 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& ? [X6] :
( rpoint(X6)
& X2 = X6 )
& ? [X7] :
( rpoint(X7)
& X3 = X7 )
& rR(X1,X0,X2)
& rR(X2,X1,X3) )
=> rR(X1,X0,X3) ),
inference(rectify,[],[f87]) ).
fof(f87,axiom,
! [X389,X390,X391,X392] :
( ( ? [X396] :
( rpoint(X396)
& X389 = X396 )
& ? [X395] :
( rpoint(X395)
& X390 = X395 )
& ? [X394] :
( rpoint(X394)
& X391 = X394 )
& ? [X393] :
( rpoint(X393)
& X392 = X393 )
& rR(X390,X389,X391)
& rR(X391,X390,X392) )
=> rR(X390,X389,X392) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(89), 0), imp(cond(axiom(89), 0)))') ).
fof(f2592,plain,
spl52_153,
inference(avatar_split_clause,[],[f1131,f2590]) ).
fof(f2590,plain,
( spl52_153
<=> ! [X5,X4,X7,X6] :
( ~ rR(X5,X6,X7)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rR(X5,X4,X6)
| ~ rR(X5,X4,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_153])]) ).
fof(f1131,plain,
! [X6,X7,X4,X5] :
( ~ rR(X5,X6,X7)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rR(X5,X4,X6)
| ~ rR(X5,X4,X7) ),
inference(equality_resolution,[],[f1130]) ).
fof(f1130,plain,
! [X3,X6,X7,X4,X5] :
( ~ rR(X5,X6,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X5,X4,X6)
| ~ rR(X5,X4,X3) ),
inference(equality_resolution,[],[f1129]) ).
fof(f1129,plain,
! [X2,X3,X6,X7,X4,X5] :
( ~ rR(X5,X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X5,X4,X2)
| ~ rR(X5,X4,X3) ),
inference(equality_resolution,[],[f1128]) ).
fof(f1128,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ rR(X1,X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X1,X4,X2)
| ~ rR(X1,X4,X3) ),
inference(equality_resolution,[],[f763]) ).
fof(f763,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ rR(X1,X2,X3)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7
| ~ rR(X1,X0,X2)
| ~ rR(X1,X0,X3) ),
inference(cnf_transformation,[],[f374]) ).
fof(f374,plain,
! [X0,X1,X2,X3] :
( ~ rR(X1,X2,X3)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 )
| ~ rR(X1,X0,X2)
| ~ rR(X1,X0,X3) ),
inference(flattening,[],[f373]) ).
fof(f373,plain,
! [X0,X1,X2,X3] :
( ~ rR(X1,X2,X3)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 )
| ~ rR(X1,X0,X2)
| ~ rR(X1,X0,X3) ),
inference(ennf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( rpoint(X4)
& X0 = X4 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& ? [X6] :
( rpoint(X6)
& X2 = X6 )
& ? [X7] :
( rpoint(X7)
& X3 = X7 )
& rR(X1,X0,X2)
& rR(X1,X0,X3) )
=> ~ rR(X1,X2,X3) ),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X381,X382,X383,X384] :
( ( ? [X388] :
( rpoint(X388)
& X381 = X388 )
& ? [X387] :
( rpoint(X387)
& X382 = X387 )
& ? [X386] :
( rpoint(X386)
& X383 = X386 )
& ? [X385] :
( rpoint(X385)
& X384 = X385 )
& rR(X382,X381,X383)
& rR(X382,X381,X384) )
=> ~ rR(X382,X383,X384) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(93), 0), imp(cond(axiom(93), 0)))') ).
fof(f2588,plain,
spl52_152,
inference(avatar_split_clause,[],[f1109,f2586]) ).
fof(f2586,plain,
( spl52_152
<=> ! [X3,X4,X5,X2] :
( rinside(X4,X3)
| ~ rless(vf(X2,X4),vf(X2,X5))
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rcenter(X2,X3)
| ~ ron(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_152])]) ).
fof(f1109,plain,
! [X2,X3,X4,X5] :
( rinside(X4,X3)
| ~ rless(vf(X2,X4),vf(X2,X5))
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rcenter(X2,X3)
| ~ ron(X5,X3) ),
inference(equality_resolution,[],[f1108]) ).
fof(f1108,plain,
! [X2,X3,X1,X4,X5] :
( rinside(X4,X3)
| ~ rless(vf(X2,X4),vf(X2,X1))
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rcenter(X2,X3)
| ~ ron(X1,X3) ),
inference(equality_resolution,[],[f755]) ).
fof(f755,plain,
! [X2,X3,X0,X1,X4,X5] :
( rinside(X0,X3)
| ~ rless(vf(X2,X0),vf(X2,X1))
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rcenter(X2,X3)
| ~ ron(X1,X3) ),
inference(cnf_transformation,[],[f552]) ).
fof(f552,plain,
! [X0,X1,X2,X3] :
( ( ( rless(vf(X2,X0),vf(X2,X1))
| ~ rinside(X0,X3) )
& ( rinside(X0,X3)
| ~ rless(vf(X2,X0),vf(X2,X1)) ) )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ rcenter(X2,X3)
| ~ ron(X1,X3) ),
inference(nnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0,X1,X2,X3] :
( ( rless(vf(X2,X0),vf(X2,X1))
<=> rinside(X0,X3) )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ rcenter(X2,X3)
| ~ ron(X1,X3) ),
inference(flattening,[],[f365]) ).
fof(f365,plain,
! [X0,X1,X2,X3] :
( ( rless(vf(X2,X0),vf(X2,X1))
<=> rinside(X0,X3) )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ rcenter(X2,X3)
| ~ ron(X1,X3) ),
inference(ennf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( rpoint(X4)
& X0 = X4 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& rcenter(X2,X3)
& ron(X1,X3) )
=> ( rless(vf(X2,X0),vf(X2,X1))
<=> rinside(X0,X3) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X2,X3,X4,X5] :
( ( ? [X7] :
( rpoint(X7)
& X2 = X7 )
& ? [X6] :
( rpoint(X6)
& X3 = X6 )
& rcenter(X4,X5)
& ron(X3,X5) )
=> ( rless(vf(X4,X2),vf(X4,X3))
<=> rinside(X2,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(186), 0), imp(cond(axiom(186), 0)))') ).
fof(f2582,plain,
spl52_151,
inference(avatar_split_clause,[],[f1107,f2580]) ).
fof(f2580,plain,
( spl52_151
<=> ! [X3,X4,X5,X2] :
( rless(vf(X2,X4),vf(X2,X5))
| ~ rinside(X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rcenter(X2,X3)
| ~ ron(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_151])]) ).
fof(f1107,plain,
! [X2,X3,X4,X5] :
( rless(vf(X2,X4),vf(X2,X5))
| ~ rinside(X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rcenter(X2,X3)
| ~ ron(X5,X3) ),
inference(equality_resolution,[],[f1106]) ).
fof(f1106,plain,
! [X2,X3,X1,X4,X5] :
( rless(vf(X2,X4),vf(X2,X1))
| ~ rinside(X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rcenter(X2,X3)
| ~ ron(X1,X3) ),
inference(equality_resolution,[],[f756]) ).
fof(f756,plain,
! [X2,X3,X0,X1,X4,X5] :
( rless(vf(X2,X0),vf(X2,X1))
| ~ rinside(X0,X3)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rcenter(X2,X3)
| ~ ron(X1,X3) ),
inference(cnf_transformation,[],[f552]) ).
fof(f2508,plain,
spl52_150,
inference(avatar_split_clause,[],[f1310,f2506]) ).
fof(f2506,plain,
( spl52_150
<=> ! [X5,X1,X3] :
( sK40(X1,X3,X5) != X5
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1)
| ~ rpoint(X5)
| ~ rS(X5,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_150])]) ).
fof(f1310,plain,
! [X3,X1,X5] :
( sK40(X1,X3,X5) != X5
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1)
| ~ rpoint(X5)
| ~ rS(X5,X3,X1) ),
inference(equality_resolution,[],[f1309]) ).
fof(f1309,plain,
! [X2,X3,X1,X5] :
( sK40(X1,X2,X5) != X5
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| ~ rpoint(X5)
| ~ rS(X5,X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f1308]) ).
fof(f1308,plain,
! [X2,X3,X1,X4,X5] :
( sK40(X1,X2,X4) != X4
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| ~ rpoint(X5)
| ~ rS(X4,X2,X1)
| X4 != X5
| X2 != X3 ),
inference(equality_resolution,[],[f809]) ).
fof(f809,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK40(X0,X2,X4) != X4
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| ~ rpoint(X5)
| ~ rS(X4,X2,X0)
| X4 != X5
| X2 != X3 ),
inference(cnf_transformation,[],[f576]) ).
fof(f2504,plain,
spl52_149,
inference(avatar_split_clause,[],[f1307,f2502]) ).
fof(f2502,plain,
( spl52_149
<=> ! [X5,X1,X3] :
( sK40(X1,X3,X5) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1)
| ~ rpoint(X5)
| ~ rS(X5,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_149])]) ).
fof(f1307,plain,
! [X3,X1,X5] :
( sK40(X1,X3,X5) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1)
| ~ rpoint(X5)
| ~ rS(X5,X3,X1) ),
inference(equality_resolution,[],[f1306]) ).
fof(f1306,plain,
! [X2,X3,X1,X5] :
( sK40(X1,X2,X5) != X2
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| ~ rpoint(X5)
| ~ rS(X5,X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f1305]) ).
fof(f1305,plain,
! [X2,X3,X1,X4,X5] :
( sK40(X1,X2,X4) != X2
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| ~ rpoint(X5)
| ~ rS(X4,X2,X1)
| X4 != X5
| X2 != X3 ),
inference(equality_resolution,[],[f810]) ).
fof(f810,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK40(X0,X2,X4) != X2
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| ~ rpoint(X5)
| ~ rS(X4,X2,X0)
| X4 != X5
| X2 != X3 ),
inference(cnf_transformation,[],[f576]) ).
fof(f2500,plain,
spl52_148,
inference(avatar_split_clause,[],[f1214,f2498]) ).
fof(f2498,plain,
( spl52_148
<=> ! [X5,X4,X7,X6] :
( ~ rS(X5,X7,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ ron(X6,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_148])]) ).
fof(f1214,plain,
! [X6,X7,X4,X5] :
( ~ rS(X5,X7,X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| ~ rR(X6,X5,X7)
| ~ ron(X6,X4) ),
inference(equality_resolution,[],[f1213]) ).
fof(f1213,plain,
! [X3,X6,X7,X4,X5] :
( ~ rS(X5,X7,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| ~ rline(X4)
| X3 != X4
| ~ rR(X6,X5,X7)
| ~ ron(X6,X3) ),
inference(equality_resolution,[],[f1212]) ).
fof(f1212,plain,
! [X2,X3,X6,X7,X4,X5] :
( ~ rS(X5,X2,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rR(X6,X5,X2)
| ~ ron(X6,X3) ),
inference(equality_resolution,[],[f1211]) ).
fof(f1211,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ rS(X5,X2,X3)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rR(X1,X5,X2)
| ~ ron(X1,X3) ),
inference(equality_resolution,[],[f789]) ).
fof(f789,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ rS(X0,X2,X3)
| ~ rpoint(X5)
| X0 != X5
| ~ rpoint(X6)
| X1 != X6
| ~ rpoint(X7)
| X2 != X7
| ~ rline(X4)
| X3 != X4
| ~ rR(X1,X0,X2)
| ~ ron(X1,X3) ),
inference(cnf_transformation,[],[f402]) ).
fof(f402,plain,
! [X0,X1,X2,X3,X4] :
( ~ rS(X0,X2,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| X3 != X4
| ~ rR(X1,X0,X2)
| ~ ron(X1,X3) ),
inference(flattening,[],[f401]) ).
fof(f401,plain,
! [X0,X1,X2,X3,X4] :
( ~ rS(X0,X2,X3)
| ! [X5] :
( ~ rpoint(X5)
| X0 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X1 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X2 != X7 )
| ~ rline(X4)
| X3 != X4
| ~ rR(X1,X0,X2)
| ~ ron(X1,X3) ),
inference(ennf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( rpoint(X5)
& X0 = X5 )
& ? [X6] :
( rpoint(X6)
& X1 = X6 )
& ? [X7] :
( rpoint(X7)
& X2 = X7 )
& rline(X4)
& X3 = X4
& rR(X1,X0,X2)
& ron(X1,X3) )
=> ~ rS(X0,X2,X3) ),
inference(rectify,[],[f78]) ).
fof(f78,axiom,
! [X325,X326,X327,X328,X329] :
( ( ? [X332] :
( rpoint(X332)
& X325 = X332 )
& ? [X331] :
( rpoint(X331)
& X326 = X331 )
& ? [X330] :
( rpoint(X330)
& X327 = X330 )
& rline(X329)
& X328 = X329
& rR(X326,X325,X327)
& ron(X326,X328) )
=> ~ rS(X325,X327,X328) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))') ).
fof(f2496,plain,
( spl52_147
| ~ spl52_5
| ~ spl52_16
| ~ spl52_95 ),
inference(avatar_split_clause,[],[f2172,f2090,f1653,f1602,f2494]) ).
fof(f1653,plain,
( spl52_16
<=> ! [X0] :
( ~ ron(vd1124,X0)
| ~ rline(X0)
| ~ ron(vd1126,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_16])]) ).
fof(f2090,plain,
( spl52_95
<=> ! [X4,X3] :
( ron(X3,sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_95])]) ).
fof(f2172,plain,
( ! [X0] :
( ~ rpoint(vd1124)
| ~ rpoint(X0)
| vd1124 = X0
| ~ rline(sK10(vd1124,X0))
| ~ ron(vd1126,sK10(vd1124,X0)) )
| ~ spl52_16
| ~ spl52_95 ),
inference(resolution,[],[f2091,f1654]) ).
fof(f1654,plain,
( ! [X0] :
( ~ ron(vd1124,X0)
| ~ rline(X0)
| ~ ron(vd1126,X0) )
| ~ spl52_16 ),
inference(avatar_component_clause,[],[f1653]) ).
fof(f2091,plain,
( ! [X3,X4] :
( ron(X3,sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 )
| ~ spl52_95 ),
inference(avatar_component_clause,[],[f2090]) ).
fof(f2492,plain,
spl52_146,
inference(avatar_split_clause,[],[f1111,f2490]) ).
fof(f2490,plain,
( spl52_146
<=> ! [X3,X4,X5,X2] :
( rintersect(X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ ron(X4,X2)
| ~ rinside(X5,X2)
| ~ rinside(X4,X3)
| ~ ron(X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_146])]) ).
fof(f1111,plain,
! [X2,X3,X4,X5] :
( rintersect(X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ ron(X4,X2)
| ~ rinside(X5,X2)
| ~ rinside(X4,X3)
| ~ ron(X5,X3) ),
inference(equality_resolution,[],[f1110]) ).
fof(f1110,plain,
! [X2,X3,X1,X4,X5] :
( rintersect(X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ ron(X4,X2)
| ~ rinside(X1,X2)
| ~ rinside(X4,X3)
| ~ ron(X1,X3) ),
inference(equality_resolution,[],[f757]) ).
fof(f757,plain,
! [X2,X3,X0,X1,X4,X5] :
( rintersect(X2,X3)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ ron(X0,X2)
| ~ rinside(X1,X2)
| ~ rinside(X0,X3)
| ~ ron(X1,X3) ),
inference(cnf_transformation,[],[f368]) ).
fof(f368,plain,
! [X0,X1,X2,X3] :
( rintersect(X2,X3)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ ron(X0,X2)
| ~ rinside(X1,X2)
| ~ rinside(X0,X3)
| ~ ron(X1,X3) ),
inference(flattening,[],[f367]) ).
fof(f367,plain,
! [X0,X1,X2,X3] :
( rintersect(X2,X3)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ ron(X0,X2)
| ~ rinside(X1,X2)
| ~ rinside(X0,X3)
| ~ ron(X1,X3) ),
inference(ennf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( rpoint(X4)
& X0 = X4 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& ron(X0,X2)
& rinside(X1,X2)
& rinside(X0,X3)
& ron(X1,X3) )
=> rintersect(X2,X3) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X14,X15,X16,X17] :
( ( ? [X19] :
( rpoint(X19)
& X14 = X19 )
& ? [X18] :
( rpoint(X18)
& X15 = X18 )
& ron(X14,X16)
& rinside(X15,X16)
& rinside(X14,X17)
& ron(X15,X17) )
=> rintersect(X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(135), 0), imp(cond(axiom(135), 0)))') ).
fof(f2488,plain,
spl52_145,
inference(avatar_split_clause,[],[f1031,f2486]) ).
fof(f2486,plain,
( spl52_145
<=> ! [X6,X5,X1] :
( rpoint(sK23(X5,X6))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1)
| X5 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_145])]) ).
fof(f1031,plain,
! [X1,X6,X5] :
( rpoint(sK23(X5,X6))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1)
| X5 = X6 ),
inference(equality_resolution,[],[f1030]) ).
fof(f1030,plain,
! [X3,X1,X6,X5] :
( rpoint(sK23(X5,X3))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X5,X1)
| ~ ron(X3,X1)
| X3 = X5 ),
inference(equality_resolution,[],[f1029]) ).
fof(f1029,plain,
! [X2,X3,X1,X6,X5] :
( rpoint(sK23(X2,X3))
| ~ rline(X1)
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X1)
| ~ ron(X3,X1)
| X2 = X3 ),
inference(equality_resolution,[],[f713]) ).
fof(f713,plain,
! [X2,X3,X0,X1,X6,X5] :
( rpoint(sK23(X2,X3))
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(cnf_transformation,[],[f531]) ).
fof(f2484,plain,
spl52_144,
inference(avatar_split_clause,[],[f1025,f2482]) ).
fof(f2482,plain,
( spl52_144
<=> ! [X6,X5,X1] :
( rpoint(sK22(X5,X6))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1)
| X5 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_144])]) ).
fof(f1025,plain,
! [X1,X6,X5] :
( rpoint(sK22(X5,X6))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1)
| X5 = X6 ),
inference(equality_resolution,[],[f1024]) ).
fof(f1024,plain,
! [X3,X1,X6,X5] :
( rpoint(sK22(X5,X3))
| ~ rline(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X5,X1)
| ~ ron(X3,X1)
| X3 = X5 ),
inference(equality_resolution,[],[f1023]) ).
fof(f1023,plain,
! [X2,X3,X1,X6,X5] :
( rpoint(sK22(X2,X3))
| ~ rline(X1)
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X1)
| ~ ron(X3,X1)
| X2 = X3 ),
inference(equality_resolution,[],[f711]) ).
fof(f711,plain,
! [X2,X3,X0,X1,X6,X5] :
( rpoint(sK22(X2,X3))
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X0)
| ~ ron(X3,X0)
| X2 = X3 ),
inference(cnf_transformation,[],[f528]) ).
fof(f2444,plain,
spl52_143,
inference(avatar_split_clause,[],[f1347,f2442]) ).
fof(f2442,plain,
( spl52_143
<=> ! [X5,X1,X3] :
( sK42(X1,X3,X5) != X5
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| ~ ron(X3,X1)
| ~ ron(X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_143])]) ).
fof(f1347,plain,
! [X3,X1,X5] :
( sK42(X1,X3,X5) != X5
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| ~ ron(X3,X1)
| ~ ron(X5,X1) ),
inference(equality_resolution,[],[f1346]) ).
fof(f1346,plain,
! [X3,X1,X4,X5] :
( sK42(X1,X3,X4) != X4
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X3,X1)
| ~ ron(X4,X1) ),
inference(equality_resolution,[],[f1345]) ).
fof(f1345,plain,
! [X2,X3,X1,X4,X5] :
( sK42(X1,X2,X4) != X4
| ~ rline(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X1)
| ~ ron(X4,X1) ),
inference(equality_resolution,[],[f821]) ).
fof(f821,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK42(X0,X2,X4) != X4
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X0)
| ~ ron(X4,X0) ),
inference(cnf_transformation,[],[f582]) ).
fof(f582,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rpoint(sK42(X0,X2,X4))
& ron(sK42(X0,X2,X4),X0)
& sK42(X0,X2,X4) != X2
& sK42(X0,X2,X4) != X4 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X0)
| ~ ron(X4,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f436,f581]) ).
fof(f581,plain,
! [X0,X2,X4] :
( ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X2 != X6
& X4 != X6 )
=> ( rpoint(sK42(X0,X2,X4))
& ron(sK42(X0,X2,X4),X0)
& sK42(X0,X2,X4) != X2
& sK42(X0,X2,X4) != X4 ) ),
introduced(choice_axiom,[]) ).
fof(f436,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X2 != X6
& X4 != X6 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X0)
| ~ ron(X4,X0) ),
inference(flattening,[],[f435]) ).
fof(f435,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X2 != X6
& X4 != X6 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X0)
| ~ ron(X4,X0) ),
inference(ennf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& X2 = X3
& rpoint(X5)
& X4 = X5
& ron(X2,X0)
& ron(X4,X0) )
=> ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X2 != X6
& X4 != X6 ) ),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X556,X557,X558,X559,X560,X561] :
( ( rline(X557)
& X556 = X557
& rpoint(X559)
& X558 = X559
& rpoint(X561)
& X560 = X561
& ron(X558,X556)
& ron(X560,X556) )
=> ? [X562] :
( rpoint(X562)
& ron(X562,X556)
& X558 != X562
& X560 != X562 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(19), 0), imp(cond(axiom(19), 0)))') ).
fof(f2440,plain,
spl52_142,
inference(avatar_split_clause,[],[f1344,f2438]) ).
fof(f2438,plain,
( spl52_142
<=> ! [X5,X1,X3] :
( sK42(X1,X3,X5) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| ~ ron(X3,X1)
| ~ ron(X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_142])]) ).
fof(f1344,plain,
! [X3,X1,X5] :
( sK42(X1,X3,X5) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| ~ ron(X3,X1)
| ~ ron(X5,X1) ),
inference(equality_resolution,[],[f1343]) ).
fof(f1343,plain,
! [X3,X1,X4,X5] :
( sK42(X1,X3,X4) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X3,X1)
| ~ ron(X4,X1) ),
inference(equality_resolution,[],[f1342]) ).
fof(f1342,plain,
! [X2,X3,X1,X4,X5] :
( sK42(X1,X2,X4) != X2
| ~ rline(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X1)
| ~ ron(X4,X1) ),
inference(equality_resolution,[],[f822]) ).
fof(f822,plain,
! [X2,X3,X0,X1,X4,X5] :
( sK42(X0,X2,X4) != X2
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X0)
| ~ ron(X4,X0) ),
inference(cnf_transformation,[],[f582]) ).
fof(f2436,plain,
spl52_141,
inference(avatar_split_clause,[],[f1341,f2434]) ).
fof(f2434,plain,
( spl52_141
<=> ! [X5,X1,X3] :
( ron(sK42(X1,X3,X5),X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| ~ ron(X3,X1)
| ~ ron(X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_141])]) ).
fof(f1341,plain,
! [X3,X1,X5] :
( ron(sK42(X1,X3,X5),X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| ~ ron(X3,X1)
| ~ ron(X5,X1) ),
inference(equality_resolution,[],[f1340]) ).
fof(f1340,plain,
! [X3,X1,X4,X5] :
( ron(sK42(X1,X3,X4),X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X3,X1)
| ~ ron(X4,X1) ),
inference(equality_resolution,[],[f1339]) ).
fof(f1339,plain,
! [X2,X3,X1,X4,X5] :
( ron(sK42(X1,X2,X4),X1)
| ~ rline(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X1)
| ~ ron(X4,X1) ),
inference(equality_resolution,[],[f823]) ).
fof(f823,plain,
! [X2,X3,X0,X1,X4,X5] :
( ron(sK42(X0,X2,X4),X0)
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X0)
| ~ ron(X4,X0) ),
inference(cnf_transformation,[],[f582]) ).
fof(f2432,plain,
spl52_140,
inference(avatar_split_clause,[],[f1301,f2430]) ).
fof(f2430,plain,
( spl52_140
<=> ! [X5,X1,X3] :
( rpoint(sK40(X1,X3,X5))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1)
| ~ rpoint(X5)
| ~ rS(X5,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_140])]) ).
fof(f1301,plain,
! [X3,X1,X5] :
( rpoint(sK40(X1,X3,X5))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1)
| ~ rpoint(X5)
| ~ rS(X5,X3,X1) ),
inference(equality_resolution,[],[f1300]) ).
fof(f1300,plain,
! [X2,X3,X1,X5] :
( rpoint(sK40(X1,X2,X5))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| ~ rpoint(X5)
| ~ rS(X5,X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f1299]) ).
fof(f1299,plain,
! [X2,X3,X1,X4,X5] :
( rpoint(sK40(X1,X2,X4))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| ~ rpoint(X5)
| ~ rS(X4,X2,X1)
| X4 != X5
| X2 != X3 ),
inference(equality_resolution,[],[f812]) ).
fof(f812,plain,
! [X2,X3,X0,X1,X4,X5] :
( rpoint(sK40(X0,X2,X4))
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| ~ rpoint(X5)
| ~ rS(X4,X2,X0)
| X4 != X5
| X2 != X3 ),
inference(cnf_transformation,[],[f576]) ).
fof(f2428,plain,
spl52_139,
inference(avatar_split_clause,[],[f1127,f2426]) ).
fof(f2426,plain,
( spl52_139
<=> ! [X6,X5,X1] :
( sK34(X1,X5,X6) != X6
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_139])]) ).
fof(f1127,plain,
! [X1,X6,X5] :
( sK34(X1,X5,X6) != X6
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1) ),
inference(equality_resolution,[],[f1126]) ).
fof(f1126,plain,
! [X3,X1,X6,X5] :
( sK34(X1,X5,X3) != X3
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X5,X1)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1125]) ).
fof(f1125,plain,
! [X2,X3,X1,X6,X5] :
( sK34(X1,X2,X3) != X3
| ~ rcircle(X1)
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X1)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f759]) ).
fof(f759,plain,
! [X2,X3,X0,X1,X6,X5] :
( sK34(X0,X2,X3) != X3
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X0)
| ~ ron(X3,X0) ),
inference(cnf_transformation,[],[f555]) ).
fof(f555,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK34(X0,X2,X3))
& ron(sK34(X0,X2,X3),X0)
& sK34(X0,X2,X3) != X2
& sK34(X0,X2,X3) != X3 )
| ~ rcircle(X1)
| X0 != X1
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X3 != X6 )
| ~ ron(X2,X0)
| ~ ron(X3,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f553,f554]) ).
fof(f554,plain,
! [X0,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4
& X3 != X4 )
=> ( rpoint(sK34(X0,X2,X3))
& ron(sK34(X0,X2,X3),X0)
& sK34(X0,X2,X3) != X2
& sK34(X0,X2,X3) != X3 ) ),
introduced(choice_axiom,[]) ).
fof(f553,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4
& X3 != X4 )
| ~ rcircle(X1)
| X0 != X1
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X3 != X6 )
| ~ ron(X2,X0)
| ~ ron(X3,X0) ),
inference(rectify,[],[f372]) ).
fof(f372,plain,
! [X0,X1,X2,X3] :
( ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X2 != X6
& X3 != X6 )
| ~ rcircle(X1)
| X0 != X1
| ! [X4] :
( ~ rpoint(X4)
| X2 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X3 != X5 )
| ~ ron(X2,X0)
| ~ ron(X3,X0) ),
inference(flattening,[],[f371]) ).
fof(f371,plain,
! [X0,X1,X2,X3] :
( ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X2 != X6
& X3 != X6 )
| ~ rcircle(X1)
| X0 != X1
| ! [X4] :
( ~ rpoint(X4)
| X2 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X3 != X5 )
| ~ ron(X2,X0)
| ~ ron(X3,X0) ),
inference(ennf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& ? [X4] :
( rpoint(X4)
& X2 = X4 )
& ? [X5] :
( rpoint(X5)
& X3 = X5 )
& ron(X2,X0)
& ron(X3,X0) )
=> ? [X6] :
( rpoint(X6)
& ron(X6,X0)
& X2 != X6
& X3 != X6 ) ),
inference(rectify,[],[f97]) ).
fof(f97,axiom,
! [X463,X464,X465,X466] :
( ( rcircle(X464)
& X463 = X464
& ? [X468] :
( rpoint(X468)
& X465 = X468 )
& ? [X467] :
( rpoint(X467)
& X466 = X467 )
& ron(X465,X463)
& ron(X466,X463) )
=> ? [X469] :
( rpoint(X469)
& ron(X469,X463)
& X465 != X469
& X466 != X469 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(45), 0), imp(cond(axiom(45), 0)))') ).
fof(f2424,plain,
spl52_138,
inference(avatar_split_clause,[],[f1124,f2422]) ).
fof(f2422,plain,
( spl52_138
<=> ! [X6,X5,X1] :
( sK34(X1,X5,X6) != X5
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_138])]) ).
fof(f1124,plain,
! [X1,X6,X5] :
( sK34(X1,X5,X6) != X5
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1) ),
inference(equality_resolution,[],[f1123]) ).
fof(f1123,plain,
! [X3,X1,X6,X5] :
( sK34(X1,X5,X3) != X5
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X5,X1)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1122]) ).
fof(f1122,plain,
! [X2,X3,X1,X6,X5] :
( sK34(X1,X2,X3) != X2
| ~ rcircle(X1)
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X1)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f760]) ).
fof(f760,plain,
! [X2,X3,X0,X1,X6,X5] :
( sK34(X0,X2,X3) != X2
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X0)
| ~ ron(X3,X0) ),
inference(cnf_transformation,[],[f555]) ).
fof(f2420,plain,
spl52_137,
inference(avatar_split_clause,[],[f1121,f2418]) ).
fof(f2418,plain,
( spl52_137
<=> ! [X6,X5,X1] :
( ron(sK34(X1,X5,X6),X1)
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_137])]) ).
fof(f1121,plain,
! [X1,X6,X5] :
( ron(sK34(X1,X5,X6),X1)
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1) ),
inference(equality_resolution,[],[f1120]) ).
fof(f1120,plain,
! [X3,X1,X6,X5] :
( ron(sK34(X1,X5,X3),X1)
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X5,X1)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1119]) ).
fof(f1119,plain,
! [X2,X3,X1,X6,X5] :
( ron(sK34(X1,X2,X3),X1)
| ~ rcircle(X1)
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X1)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f761]) ).
fof(f761,plain,
! [X2,X3,X0,X1,X6,X5] :
( ron(sK34(X0,X2,X3),X0)
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X0)
| ~ ron(X3,X0) ),
inference(cnf_transformation,[],[f555]) ).
fof(f2416,plain,
spl52_136,
inference(avatar_split_clause,[],[f1056,f2414]) ).
fof(f2414,plain,
( spl52_136
<=> ! [X1,X3] :
( vf(X1,X3) = vf(X3,vskolem1052(X1,X1,X3,X3))
| ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_136])]) ).
fof(f1056,plain,
! [X3,X1] :
( vf(X1,X3) = vf(X3,vskolem1052(X1,X1,X3,X3))
| ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X3 ),
inference(equality_resolution,[],[f1055]) ).
fof(f1055,plain,
! [X2,X3,X1] :
( vf(X1,X2) = vf(X2,vskolem1052(X1,X1,X2,X3))
| ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X2
| X2 != X3 ),
inference(equality_resolution,[],[f722]) ).
fof(f722,plain,
! [X2,X3,X0,X1] :
( vf(X0,X2) = vf(X2,vskolem1052(X0,X1,X2,X3))
| ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3 ),
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0,X1,X2,X3] :
( vf(X0,X2) = vf(X2,vskolem1052(X0,X1,X2,X3))
| ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3 ),
inference(flattening,[],[f339]) ).
fof(f339,plain,
! [X0,X1,X2,X3] :
( vf(X0,X2) = vf(X2,vskolem1052(X0,X1,X2,X3))
| ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3 ),
inference(ennf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> vf(X0,X2) = vf(X2,vskolem1052(X0,X1,X2,X3)) ),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X152,X153,X154,X155] :
( ( rpoint(X153)
& X152 = X153
& rpoint(X155)
& X152 != X154
& X154 = X155 )
=> vf(X154,vskolem1052(X152,X153,X154,X155)) = vf(X152,X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 1)') ).
fof(f2398,plain,
spl52_135,
inference(avatar_split_clause,[],[f1338,f2396]) ).
fof(f2396,plain,
( spl52_135
<=> ! [X5,X1,X3] :
( rpoint(sK42(X1,X3,X5))
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| ~ ron(X3,X1)
| ~ ron(X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_135])]) ).
fof(f1338,plain,
! [X3,X1,X5] :
( rpoint(sK42(X1,X3,X5))
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| ~ ron(X3,X1)
| ~ ron(X5,X1) ),
inference(equality_resolution,[],[f1337]) ).
fof(f1337,plain,
! [X3,X1,X4,X5] :
( rpoint(sK42(X1,X3,X4))
| ~ rline(X1)
| ~ rpoint(X3)
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X3,X1)
| ~ ron(X4,X1) ),
inference(equality_resolution,[],[f1336]) ).
fof(f1336,plain,
! [X2,X3,X1,X4,X5] :
( rpoint(sK42(X1,X2,X4))
| ~ rline(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X1)
| ~ ron(X4,X1) ),
inference(equality_resolution,[],[f824]) ).
fof(f824,plain,
! [X2,X3,X0,X1,X4,X5] :
( rpoint(sK42(X0,X2,X4))
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X5)
| X4 != X5
| ~ ron(X2,X0)
| ~ ron(X4,X0) ),
inference(cnf_transformation,[],[f582]) ).
fof(f2394,plain,
spl52_134,
inference(avatar_split_clause,[],[f1118,f2392]) ).
fof(f2392,plain,
( spl52_134
<=> ! [X6,X5,X1] :
( rpoint(sK34(X1,X5,X6))
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_134])]) ).
fof(f1118,plain,
! [X1,X6,X5] :
( rpoint(sK34(X1,X5,X6))
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ ron(X5,X1)
| ~ ron(X6,X1) ),
inference(equality_resolution,[],[f1117]) ).
fof(f1117,plain,
! [X3,X1,X6,X5] :
( rpoint(sK34(X1,X5,X3))
| ~ rcircle(X1)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X5,X1)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1116]) ).
fof(f1116,plain,
! [X2,X3,X1,X6,X5] :
( rpoint(sK34(X1,X2,X3))
| ~ rcircle(X1)
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X1)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f762]) ).
fof(f762,plain,
! [X2,X3,X0,X1,X6,X5] :
( rpoint(sK34(X0,X2,X3))
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X5)
| X2 != X5
| ~ rpoint(X6)
| X3 != X6
| ~ ron(X2,X0)
| ~ ron(X3,X0) ),
inference(cnf_transformation,[],[f555]) ).
fof(f2376,plain,
spl52_133,
inference(avatar_split_clause,[],[f1370,f2374]) ).
fof(f2374,plain,
( spl52_133
<=> ! [X5,X1,X3] :
( X1 = X3
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| vplus(X1,X5) != vplus(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_133])]) ).
fof(f1370,plain,
! [X3,X1,X5] :
( X1 = X3
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| vplus(X1,X5) != vplus(X3,X5) ),
inference(equality_resolution,[],[f1369]) ).
fof(f1369,plain,
! [X3,X1,X4,X5] :
( X1 = X3
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| X4 != X5
| vplus(X1,X4) != vplus(X3,X4) ),
inference(equality_resolution,[],[f1368]) ).
fof(f1368,plain,
! [X2,X3,X1,X4,X5] :
( X1 = X2
| ~ rreal(X1)
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| vplus(X2,X4) != vplus(X1,X4) ),
inference(equality_resolution,[],[f829]) ).
fof(f829,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X2
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| vplus(X0,X4) != vplus(X2,X4) ),
inference(cnf_transformation,[],[f440]) ).
fof(f440,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X2
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| vplus(X0,X4) != vplus(X2,X4) ),
inference(flattening,[],[f439]) ).
fof(f439,plain,
! [X0,X1,X2,X3,X4,X5] :
( X0 = X2
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| vplus(X0,X4) != vplus(X2,X4) ),
inference(ennf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3
& rreal(X5)
& X4 = X5
& vplus(X0,X4) = vplus(X2,X4) )
=> X0 = X2 ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X162,X163,X164,X165,X166,X167] :
( ( rreal(X163)
& X162 = X163
& rreal(X165)
& X164 = X165
& rreal(X167)
& X166 = X167
& vplus(X162,X166) = vplus(X164,X166) )
=> X162 = X164 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(156, 0), 0)') ).
fof(f2372,plain,
spl52_132,
inference(avatar_split_clause,[],[f1325,f2370]) ).
fof(f2370,plain,
( spl52_132
<=> ! [X5,X1,X3] :
( rless(vplus(X1,X5),vplus(X3,X5))
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| ~ rless(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_132])]) ).
fof(f1325,plain,
! [X3,X1,X5] :
( rless(vplus(X1,X5),vplus(X3,X5))
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| ~ rless(X1,X3) ),
inference(equality_resolution,[],[f1324]) ).
fof(f1324,plain,
! [X3,X1,X4,X5] :
( rless(vplus(X1,X4),vplus(X3,X4))
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| X4 != X5
| ~ rless(X1,X3) ),
inference(equality_resolution,[],[f1323]) ).
fof(f1323,plain,
! [X2,X3,X1,X4,X5] :
( rless(vplus(X1,X4),vplus(X2,X4))
| ~ rreal(X1)
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| ~ rless(X1,X2) ),
inference(equality_resolution,[],[f816]) ).
fof(f816,plain,
! [X2,X3,X0,X1,X4,X5] :
( rless(vplus(X0,X4),vplus(X2,X4))
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| ~ rless(X0,X2) ),
inference(cnf_transformation,[],[f428]) ).
fof(f428,plain,
! [X0,X1,X2,X3,X4,X5] :
( rless(vplus(X0,X4),vplus(X2,X4))
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| ~ rless(X0,X2) ),
inference(flattening,[],[f427]) ).
fof(f427,plain,
! [X0,X1,X2,X3,X4,X5] :
( rless(vplus(X0,X4),vplus(X2,X4))
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| ~ rless(X0,X2) ),
inference(ennf_transformation,[],[f214]) ).
fof(f214,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3
& rreal(X5)
& X4 = X5
& rless(X0,X2) )
=> rless(vplus(X0,X4),vplus(X2,X4)) ),
inference(rectify,[],[f62]) ).
fof(f62,axiom,
! [X199,X200,X201,X202,X203,X204] :
( ( rreal(X200)
& X199 = X200
& rreal(X202)
& X201 = X202
& rreal(X204)
& X203 = X204
& rless(X199,X201) )
=> rless(vplus(X199,X203),vplus(X201,X203)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(153), 0), imp(cond(axiom(153), 0)))') ).
fof(f2357,plain,
( spl52_12
| ~ spl52_3
| ~ spl52_5
| ~ spl52_69
| spl52_123 ),
inference(avatar_split_clause,[],[f2253,f2223,f1907,f1602,f1592,f1635]) ).
fof(f1635,plain,
( spl52_12
<=> vd1128 = vd1124 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_12])]) ).
fof(f1592,plain,
( spl52_3
<=> rpoint(vd1128) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_3])]) ).
fof(f1907,plain,
( spl52_69
<=> ! [X4,X3] :
( rcircle(sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_69])]) ).
fof(f2223,plain,
( spl52_123
<=> rcircle(sK9(vd1124,vd1128)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_123])]) ).
fof(f2253,plain,
( ~ rpoint(vd1124)
| ~ rpoint(vd1128)
| vd1128 = vd1124
| ~ spl52_69
| spl52_123 ),
inference(resolution,[],[f2225,f1908]) ).
fof(f1908,plain,
( ! [X3,X4] :
( rcircle(sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 )
| ~ spl52_69 ),
inference(avatar_component_clause,[],[f1907]) ).
fof(f2225,plain,
( ~ rcircle(sK9(vd1124,vd1128))
| spl52_123 ),
inference(avatar_component_clause,[],[f2223]) ).
fof(f2278,plain,
spl52_131,
inference(avatar_split_clause,[],[f1335,f2276]) ).
fof(f2276,plain,
( spl52_131
<=> ! [X5,X1,X3] :
( rintersect(X5,X3)
| ~ rpoint(X1)
| ~ rcircle(X3)
| ~ rline(X5)
| ~ rinside(X1,X3)
| ~ ron(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_131])]) ).
fof(f1335,plain,
! [X3,X1,X5] :
( rintersect(X5,X3)
| ~ rpoint(X1)
| ~ rcircle(X3)
| ~ rline(X5)
| ~ rinside(X1,X3)
| ~ ron(X1,X5) ),
inference(equality_resolution,[],[f1334]) ).
fof(f1334,plain,
! [X3,X1,X4,X5] :
( rintersect(X4,X3)
| ~ rpoint(X1)
| ~ rcircle(X3)
| ~ rline(X5)
| X4 != X5
| ~ rinside(X1,X3)
| ~ ron(X1,X4) ),
inference(equality_resolution,[],[f1333]) ).
fof(f1333,plain,
! [X2,X3,X1,X4,X5] :
( rintersect(X4,X2)
| ~ rpoint(X1)
| ~ rcircle(X3)
| X2 != X3
| ~ rline(X5)
| X4 != X5
| ~ rinside(X1,X2)
| ~ ron(X1,X4) ),
inference(equality_resolution,[],[f820]) ).
fof(f820,plain,
! [X2,X3,X0,X1,X4,X5] :
( rintersect(X4,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rline(X5)
| X4 != X5
| ~ rinside(X0,X2)
| ~ ron(X0,X4) ),
inference(cnf_transformation,[],[f434]) ).
fof(f434,plain,
! [X0,X1,X2,X3,X4,X5] :
( rintersect(X4,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rline(X5)
| X4 != X5
| ~ rinside(X0,X2)
| ~ ron(X0,X4) ),
inference(flattening,[],[f433]) ).
fof(f433,plain,
! [X0,X1,X2,X3,X4,X5] :
( rintersect(X4,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rline(X5)
| X4 != X5
| ~ rinside(X0,X2)
| ~ ron(X0,X4) ),
inference(ennf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rpoint(X1)
& X0 = X1
& rcircle(X3)
& X2 = X3
& rline(X5)
& X4 = X5
& rinside(X0,X2)
& ron(X0,X4) )
=> rintersect(X4,X2) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X133,X134,X135,X136,X137,X138] :
( ( rpoint(X134)
& X133 = X134
& rcircle(X136)
& X135 = X136
& rline(X138)
& X137 = X138
& rinside(X133,X135)
& ron(X133,X137) )
=> rintersect(X137,X135) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(131), 0), imp(cond(axiom(131), 0)))') ).
fof(f2274,plain,
spl52_130,
inference(avatar_split_clause,[],[f1328,f2272]) ).
fof(f2272,plain,
( spl52_130
<=> ! [X5,X1,X3] :
( rless(X1,X5)
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| ~ rless(X1,X3)
| ~ rless(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_130])]) ).
fof(f1328,plain,
! [X3,X1,X5] :
( rless(X1,X5)
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| ~ rless(X1,X3)
| ~ rless(X3,X5) ),
inference(equality_resolution,[],[f1327]) ).
fof(f1327,plain,
! [X3,X1,X4,X5] :
( rless(X1,X4)
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rreal(X5)
| X4 != X5
| ~ rless(X1,X3)
| ~ rless(X3,X4) ),
inference(equality_resolution,[],[f1326]) ).
fof(f1326,plain,
! [X2,X3,X1,X4,X5] :
( rless(X1,X4)
| ~ rreal(X1)
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| ~ rless(X1,X2)
| ~ rless(X2,X4) ),
inference(equality_resolution,[],[f817]) ).
fof(f817,plain,
! [X2,X3,X0,X1,X4,X5] :
( rless(X0,X4)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| ~ rless(X0,X2)
| ~ rless(X2,X4) ),
inference(cnf_transformation,[],[f430]) ).
fof(f430,plain,
! [X0,X1,X2,X3,X4,X5] :
( rless(X0,X4)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| ~ rless(X0,X2)
| ~ rless(X2,X4) ),
inference(flattening,[],[f429]) ).
fof(f429,plain,
! [X0,X1,X2,X3,X4,X5] :
( rless(X0,X4)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rreal(X5)
| X4 != X5
| ~ rless(X0,X2)
| ~ rless(X2,X4) ),
inference(ennf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3
& rreal(X5)
& X4 = X5
& rless(X0,X2)
& rless(X2,X4) )
=> rless(X0,X4) ),
inference(rectify,[],[f63]) ).
fof(f63,axiom,
! [X205,X206,X207,X208,X209,X210] :
( ( rreal(X206)
& X205 = X206
& rreal(X208)
& X207 = X208
& rreal(X210)
& X209 = X210
& rless(X205,X207)
& rless(X207,X209) )
=> rless(X205,X209) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(151), 0), imp(cond(axiom(151), 0)))') ).
fof(f2270,plain,
spl52_129,
inference(avatar_split_clause,[],[f1022,f2268]) ).
fof(f2268,plain,
( spl52_129
<=> ! [X6,X4,X5] :
( sK21(X4,X5,X6) = vg(X4,X5,X6)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_129])]) ).
fof(f1022,plain,
! [X6,X4,X5] :
( sK21(X4,X5,X6) = vg(X4,X5,X6)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ),
inference(equality_resolution,[],[f1021]) ).
fof(f1021,plain,
! [X2,X6,X4,X5] :
( sK21(X4,X5,X2) = vg(X4,X5,X2)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f1020]) ).
fof(f1020,plain,
! [X2,X1,X6,X4,X5] :
( sK21(X4,X1,X2) = vg(X4,X1,X2)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f708]) ).
fof(f708,plain,
! [X2,X0,X1,X6,X4,X5] :
( vg(X0,X1,X2) = sK21(X0,X1,X2)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(cnf_transformation,[],[f525]) ).
fof(f525,plain,
! [X0,X1,X2] :
( ( rreal(sK21(X0,X1,X2))
& vg(X0,X1,X2) = sK21(X0,X1,X2) )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f523,f524]) ).
fof(f524,plain,
! [X0,X1,X2] :
( ? [X3] :
( rreal(X3)
& vg(X0,X1,X2) = X3 )
=> ( rreal(sK21(X0,X1,X2))
& vg(X0,X1,X2) = sK21(X0,X1,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f523,plain,
! [X0,X1,X2] :
( ? [X3] :
( rreal(X3)
& vg(X0,X1,X2) = X3 )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 ) ),
inference(rectify,[],[f322]) ).
fof(f322,plain,
! [X0,X1,X2] :
( ? [X6] :
( rreal(X6)
& vg(X0,X1,X2) = X6 )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 ) ),
inference(flattening,[],[f321]) ).
fof(f321,plain,
! [X0,X1,X2] :
( ? [X6] :
( rreal(X6)
& vg(X0,X1,X2) = X6 )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 ) ),
inference(ennf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 ) )
=> ? [X6] :
( rreal(X6)
& vg(X0,X1,X2) = X6 ) ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X695,X696,X697] :
( ( ? [X700] :
( rpoint(X700)
& X695 = X700 )
& ? [X699] :
( rpoint(X699)
& X696 = X699 )
& ? [X698] :
( rpoint(X698)
& X697 = X698 ) )
=> ? [X701] :
( rreal(X701)
& vg(X695,X696,X697) = X701 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))') ).
fof(f2266,plain,
spl52_128,
inference(avatar_split_clause,[],[f1004,f2264]) ).
fof(f2264,plain,
( spl52_128
<=> ! [X4,X5,X3] :
( vg(X3,X4,X5) = vg(X3,X5,X4)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_128])]) ).
fof(f1004,plain,
! [X3,X4,X5] :
( vg(X3,X4,X5) = vg(X3,X5,X4)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f1003]) ).
fof(f1003,plain,
! [X2,X3,X4,X5] :
( vg(X3,X4,X2) = vg(X3,X2,X4)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X2 != X5 ),
inference(equality_resolution,[],[f1002]) ).
fof(f1002,plain,
! [X2,X3,X1,X4,X5] :
( vg(X3,X2,X1) = vg(X3,X1,X2)
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5 ),
inference(equality_resolution,[],[f702]) ).
fof(f702,plain,
! [X2,X3,X0,X1,X4,X5] :
( vg(X0,X1,X2) = vg(X0,X2,X1)
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5 ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0,X1,X2] :
( ( vg(X0,X1,X2) = vg(X2,X0,X1)
& vg(X0,X1,X2) = vg(X0,X2,X1) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 ) ),
inference(flattening,[],[f317]) ).
fof(f317,plain,
! [X0,X1,X2] :
( ( vg(X0,X1,X2) = vg(X2,X0,X1)
& vg(X0,X1,X2) = vg(X0,X2,X1) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 ) ),
inference(ennf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 ) )
=> ( vg(X0,X1,X2) = vg(X2,X0,X1)
& vg(X0,X1,X2) = vg(X0,X2,X1) ) ),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X671,X672,X673] :
( ( ? [X676] :
( rpoint(X676)
& X671 = X676 )
& ? [X675] :
( rpoint(X675)
& X672 = X675 )
& ? [X674] :
( rpoint(X674)
& X673 = X674 ) )
=> ( vg(X671,X672,X673) = vg(X673,X671,X672)
& vg(X671,X672,X673) = vg(X671,X673,X672) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(176), 0), imp(cond(axiom(176), 0)))') ).
fof(f2262,plain,
spl52_127,
inference(avatar_split_clause,[],[f1001,f2260]) ).
fof(f2260,plain,
( spl52_127
<=> ! [X4,X5,X3] :
( vg(X3,X4,X5) = vg(X5,X3,X4)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_127])]) ).
fof(f1001,plain,
! [X3,X4,X5] :
( vg(X3,X4,X5) = vg(X5,X3,X4)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5) ),
inference(equality_resolution,[],[f1000]) ).
fof(f1000,plain,
! [X2,X3,X4,X5] :
( vg(X3,X4,X2) = vg(X2,X3,X4)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X2 != X5 ),
inference(equality_resolution,[],[f999]) ).
fof(f999,plain,
! [X2,X3,X1,X4,X5] :
( vg(X3,X1,X2) = vg(X2,X3,X1)
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5 ),
inference(equality_resolution,[],[f703]) ).
fof(f703,plain,
! [X2,X3,X0,X1,X4,X5] :
( vg(X0,X1,X2) = vg(X2,X0,X1)
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5 ),
inference(cnf_transformation,[],[f318]) ).
fof(f2252,plain,
spl52_126,
inference(avatar_split_clause,[],[f1145,f2250]) ).
fof(f2250,plain,
( spl52_126
<=> ! [X4,X5,X3] :
( rS(X5,X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rline(X3)
| ~ rS(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_126])]) ).
fof(f1145,plain,
! [X3,X4,X5] :
( rS(X5,X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rline(X3)
| ~ rS(X4,X5,X3) ),
inference(equality_resolution,[],[f1144]) ).
fof(f1144,plain,
! [X2,X3,X4,X5] :
( rS(X5,X4,X2)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rline(X3)
| X2 != X3
| ~ rS(X4,X5,X2) ),
inference(equality_resolution,[],[f1143]) ).
fof(f1143,plain,
! [X2,X3,X1,X4,X5] :
( rS(X1,X4,X2)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rline(X3)
| X2 != X3
| ~ rS(X4,X1,X2) ),
inference(equality_resolution,[],[f767]) ).
fof(f767,plain,
! [X2,X3,X0,X1,X4,X5] :
( rS(X1,X0,X2)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rline(X3)
| X2 != X3
| ~ rS(X0,X1,X2) ),
inference(cnf_transformation,[],[f382]) ).
fof(f382,plain,
! [X0,X1,X2,X3] :
( rS(X1,X0,X2)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ rline(X3)
| X2 != X3
| ~ rS(X0,X1,X2) ),
inference(flattening,[],[f381]) ).
fof(f381,plain,
! [X0,X1,X2,X3] :
( rS(X1,X0,X2)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ rline(X3)
| X2 != X3
| ~ rS(X0,X1,X2) ),
inference(ennf_transformation,[],[f189]) ).
fof(f189,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( rpoint(X4)
& X0 = X4 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& rline(X3)
& X2 = X3
& rS(X0,X1,X2) )
=> rS(X1,X0,X2) ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X371,X372,X373,X374] :
( ( ? [X376] :
( rpoint(X376)
& X371 = X376 )
& ? [X375] :
( rpoint(X375)
& X372 = X375 )
& rline(X374)
& X373 = X374
& rS(X371,X372,X373) )
=> rS(X372,X371,X373) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(97), 0), imp(cond(axiom(97), 0)))') ).
fof(f2248,plain,
spl52_125,
inference(avatar_split_clause,[],[f998,f2246]) ).
fof(f2246,plain,
( spl52_125
<=> ! [X4,X5,X3] :
( ~ rR(X3,X4,X5)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_125])]) ).
fof(f998,plain,
! [X3,X4,X5] :
( ~ rR(X3,X4,X5)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X3,X5) ),
inference(equality_resolution,[],[f997]) ).
fof(f997,plain,
! [X2,X3,X4,X5] :
( ~ rR(X3,X4,X2)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X4,X3,X2) ),
inference(equality_resolution,[],[f996]) ).
fof(f996,plain,
! [X2,X3,X1,X4,X5] :
( ~ rR(X3,X1,X2)
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X3,X2) ),
inference(equality_resolution,[],[f698]) ).
fof(f698,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ rR(X0,X1,X2)
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X0,X2) ),
inference(cnf_transformation,[],[f316]) ).
fof(f316,plain,
! [X0,X1,X2] :
( ( rR(X1,X2,X0)
& X0 != X1
& X0 != X2
& ~ rR(X0,X1,X2) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ~ rR(X1,X0,X2) ),
inference(flattening,[],[f315]) ).
fof(f315,plain,
! [X0,X1,X2] :
( ( rR(X1,X2,X0)
& X0 != X1
& X0 != X2
& ~ rR(X0,X1,X2) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 )
| ~ rR(X1,X0,X2) ),
inference(ennf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 )
& rR(X1,X0,X2) )
=> ( rR(X1,X2,X0)
& X0 != X1
& X0 != X2
& ~ rR(X0,X1,X2) ) ),
inference(rectify,[],[f91]) ).
fof(f91,axiom,
! [X421,X422,X423] :
( ( ? [X426] :
( rpoint(X426)
& X421 = X426 )
& ? [X425] :
( rpoint(X425)
& X422 = X425 )
& ? [X424] :
( rpoint(X424)
& X423 = X424 )
& rR(X422,X421,X423) )
=> ( rR(X422,X423,X421)
& X421 != X422
& X421 != X423
& ~ rR(X421,X422,X423) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))') ).
fof(f2244,plain,
spl52_124,
inference(avatar_split_clause,[],[f987,f2242]) ).
fof(f2242,plain,
( spl52_124
<=> ! [X4,X5,X3] :
( rR(X4,X5,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_124])]) ).
fof(f987,plain,
! [X3,X4,X5] :
( rR(X4,X5,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X3,X5) ),
inference(equality_resolution,[],[f986]) ).
fof(f986,plain,
! [X2,X3,X4,X5] :
( rR(X4,X2,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X4,X3,X2) ),
inference(equality_resolution,[],[f985]) ).
fof(f985,plain,
! [X2,X3,X1,X4,X5] :
( rR(X1,X2,X3)
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X3,X2) ),
inference(equality_resolution,[],[f701]) ).
fof(f701,plain,
! [X2,X3,X0,X1,X4,X5] :
( rR(X1,X2,X0)
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X0,X2) ),
inference(cnf_transformation,[],[f316]) ).
fof(f2226,plain,
( ~ spl52_5
| spl52_12
| ~ spl52_123
| ~ spl52_3
| ~ spl52_94
| ~ spl52_113 ),
inference(avatar_split_clause,[],[f2185,f2167,f2086,f1592,f2223,f1635,f1602]) ).
fof(f2086,plain,
( spl52_94
<=> ! [X4,X3] :
( ron(X4,sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_94])]) ).
fof(f2167,plain,
( spl52_113
<=> ! [X0] :
( ~ rpoint(X0)
| ~ ron(vd1128,sK9(vd1124,X0))
| ~ rcircle(sK9(vd1124,X0))
| vd1124 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_113])]) ).
fof(f2185,plain,
( ~ rpoint(vd1128)
| ~ rcircle(sK9(vd1124,vd1128))
| vd1128 = vd1124
| ~ rpoint(vd1124)
| ~ spl52_94
| ~ spl52_113 ),
inference(duplicate_literal_removal,[],[f2184]) ).
fof(f2184,plain,
( ~ rpoint(vd1128)
| ~ rcircle(sK9(vd1124,vd1128))
| vd1128 = vd1124
| ~ rpoint(vd1124)
| ~ rpoint(vd1128)
| vd1128 = vd1124
| ~ spl52_94
| ~ spl52_113 ),
inference(resolution,[],[f2168,f2087]) ).
fof(f2087,plain,
( ! [X3,X4] :
( ron(X4,sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 )
| ~ spl52_94 ),
inference(avatar_component_clause,[],[f2086]) ).
fof(f2168,plain,
( ! [X0] :
( ~ ron(vd1128,sK9(vd1124,X0))
| ~ rpoint(X0)
| ~ rcircle(sK9(vd1124,X0))
| vd1124 = X0 )
| ~ spl52_113 ),
inference(avatar_component_clause,[],[f2167]) ).
fof(f2217,plain,
spl52_122,
inference(avatar_split_clause,[],[f1165,f2215]) ).
fof(f2215,plain,
( spl52_122
<=> ! [X5,X4,X7,X6] :
( sP4(X4,X5,X6,X7)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_122])]) ).
fof(f1165,plain,
! [X6,X7,X4,X5] :
( sP4(X4,X5,X6,X7)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7) ),
inference(equality_resolution,[],[f1164]) ).
fof(f1164,plain,
! [X3,X6,X7,X4,X5] :
( sP4(X4,X5,X6,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| ~ rpoint(X7)
| X3 != X7 ),
inference(equality_resolution,[],[f1163]) ).
fof(f1163,plain,
! [X2,X3,X6,X7,X4,X5] :
( sP4(X4,X5,X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7 ),
inference(equality_resolution,[],[f1162]) ).
fof(f1162,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( sP4(X4,X1,X2,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7 ),
inference(equality_resolution,[],[f777]) ).
fof(f777,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sP4(X0,X1,X2,X3)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6
| ~ rpoint(X7)
| X3 != X7 ),
inference(cnf_transformation,[],[f482]) ).
fof(f482,plain,
! [X0,X1,X2,X3] :
( sP4(X0,X1,X2,X3)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 ) ),
inference(definition_folding,[],[f386,f481]) ).
fof(f481,plain,
! [X0,X1,X2,X3] :
( ? [X8] :
( rpoint(X8)
& X0 != X8
& X1 != X8
& X2 != X8
& X3 != X8 )
| ~ sP4(X0,X1,X2,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f386,plain,
! [X0,X1,X2,X3] :
( ? [X8] :
( rpoint(X8)
& X0 != X8
& X1 != X8
& X2 != X8
& X3 != X8 )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 ) ),
inference(flattening,[],[f385]) ).
fof(f385,plain,
! [X0,X1,X2,X3] :
( ? [X8] :
( rpoint(X8)
& X0 != X8
& X1 != X8
& X2 != X8
& X3 != X8 )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 )
| ! [X7] :
( ~ rpoint(X7)
| X3 != X7 ) ),
inference(ennf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( rpoint(X4)
& X0 = X4 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& ? [X6] :
( rpoint(X6)
& X2 = X6 )
& ? [X7] :
( rpoint(X7)
& X3 = X7 ) )
=> ? [X8] :
( rpoint(X8)
& X0 != X8
& X1 != X8
& X2 != X8
& X3 != X8 ) ),
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X571,X572,X573,X574] :
( ( ? [X578] :
( rpoint(X578)
& X571 = X578 )
& ? [X577] :
( rpoint(X577)
& X572 = X577 )
& ? [X576] :
( rpoint(X576)
& X573 = X576 )
& ? [X575] :
( rpoint(X575)
& X574 = X575 ) )
=> ? [X579] :
( rpoint(X579)
& X571 != X579
& X572 != X579
& X573 != X579
& X574 != X579 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(13), 0), imp(cond(axiom(13), 0)))') ).
fof(f2213,plain,
spl52_121,
inference(avatar_split_clause,[],[f1142,f2211]) ).
fof(f2211,plain,
( spl52_121
<=> ! [X4,X5,X3] :
( ~ ron(X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rline(X3)
| ~ rS(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_121])]) ).
fof(f1142,plain,
! [X3,X4,X5] :
( ~ ron(X4,X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rline(X3)
| ~ rS(X4,X5,X3) ),
inference(equality_resolution,[],[f1141]) ).
fof(f1141,plain,
! [X2,X3,X4,X5] :
( ~ ron(X4,X2)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rline(X3)
| X2 != X3
| ~ rS(X4,X5,X2) ),
inference(equality_resolution,[],[f1140]) ).
fof(f1140,plain,
! [X2,X3,X1,X4,X5] :
( ~ ron(X4,X2)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rline(X3)
| X2 != X3
| ~ rS(X4,X1,X2) ),
inference(equality_resolution,[],[f766]) ).
fof(f766,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ron(X0,X2)
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rline(X3)
| X2 != X3
| ~ rS(X0,X1,X2) ),
inference(cnf_transformation,[],[f380]) ).
fof(f380,plain,
! [X0,X1,X2,X3] :
( ~ ron(X0,X2)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ rline(X3)
| X2 != X3
| ~ rS(X0,X1,X2) ),
inference(flattening,[],[f379]) ).
fof(f379,plain,
! [X0,X1,X2,X3] :
( ~ ron(X0,X2)
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ~ rline(X3)
| X2 != X3
| ~ rS(X0,X1,X2) ),
inference(ennf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( rpoint(X4)
& X0 = X4 )
& ? [X5] :
( rpoint(X5)
& X1 = X5 )
& rline(X3)
& X2 = X3
& rS(X0,X1,X2) )
=> ~ ron(X0,X2) ),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X365,X366,X367,X368] :
( ( ? [X370] :
( rpoint(X370)
& X365 = X370 )
& ? [X369] :
( rpoint(X369)
& X366 = X369 )
& rline(X368)
& X367 = X368
& rS(X365,X366,X367) )
=> ~ ron(X365,X367) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))') ).
fof(f2209,plain,
spl52_120,
inference(avatar_split_clause,[],[f1071,f2207]) ).
fof(f2207,plain,
( spl52_120
<=> ! [X1,X3] :
( X1 = X3
| ~ rless(X3,X1)
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rless(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_120])]) ).
fof(f1071,plain,
! [X3,X1] :
( X1 = X3
| ~ rless(X3,X1)
| ~ rreal(X1)
| ~ rreal(X3)
| ~ rless(X1,X3) ),
inference(equality_resolution,[],[f1070]) ).
fof(f1070,plain,
! [X2,X3,X1] :
( X1 = X2
| ~ rless(X2,X1)
| ~ rreal(X1)
| ~ rreal(X3)
| X2 != X3
| ~ rless(X1,X2) ),
inference(equality_resolution,[],[f730]) ).
fof(f730,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ rless(X2,X0)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rless(X0,X2) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ rless(X2,X0)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rless(X0,X2) ),
inference(flattening,[],[f349]) ).
fof(f349,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ rless(X2,X0)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3
| ~ rless(X0,X2) ),
inference(ennf_transformation,[],[f173]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3
& rless(X0,X2) )
=> ( X0 = X2
| ~ rless(X2,X0) ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X64,X65,X66,X67] :
( ( rreal(X65)
& X64 = X65
& rreal(X67)
& X66 = X67
& rless(X64,X66) )
=> ( X64 = X66
| ~ rless(X66,X64) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(147), 0), imp(cond(axiom(147), 0)))') ).
fof(f2205,plain,
spl52_119,
inference(avatar_split_clause,[],[f1068,f2203]) ).
fof(f2203,plain,
( spl52_119
<=> ! [X1,X3] :
( ~ rS(sK26(X1,X3),X3,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_119])]) ).
fof(f1068,plain,
! [X3,X1] :
( ~ rS(sK26(X1,X3),X3,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ),
inference(equality_resolution,[],[f1067]) ).
fof(f1067,plain,
! [X2,X3,X1] :
( ~ rS(sK26(X1,X2),X2,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f727]) ).
fof(f727,plain,
! [X2,X3,X0,X1] :
( ~ rS(sK26(X0,X2),X2,X0)
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(cnf_transformation,[],[f537]) ).
fof(f537,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK26(X0,X2))
& ~ rS(sK26(X0,X2),X2,X0) )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f346,f536]) ).
fof(f536,plain,
! [X0,X2] :
( ? [X4] :
( rpoint(X4)
& ~ rS(X4,X2,X0) )
=> ( rpoint(sK26(X0,X2))
& ~ rS(sK26(X0,X2),X2,X0) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ~ rS(X4,X2,X0) )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(flattening,[],[f345]) ).
fof(f345,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ~ rS(X4,X2,X0) )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(ennf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& ~ ron(X2,X0)
& X2 = X3 )
=> ? [X4] :
( rpoint(X4)
& ~ rS(X4,X2,X0) ) ),
inference(rectify,[],[f100]) ).
fof(f100,axiom,
! [X478,X479,X480,X481] :
( ( rline(X479)
& X478 = X479
& rpoint(X481)
& ~ ron(X480,X478)
& X480 = X481 )
=> ? [X482] :
( rpoint(X482)
& ~ rS(X482,X480,X478) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(39), 0), imp(cond(axiom(39), 0)))') ).
fof(f2201,plain,
spl52_118,
inference(avatar_split_clause,[],[f1062,f2199]) ).
fof(f2199,plain,
( spl52_118
<=> ! [X1,X3] :
( rS(sK25(X1,X3),X3,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_118])]) ).
fof(f1062,plain,
! [X3,X1] :
( rS(sK25(X1,X3),X3,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ),
inference(equality_resolution,[],[f1061]) ).
fof(f1061,plain,
! [X2,X3,X1] :
( rS(sK25(X1,X2),X2,X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f725]) ).
fof(f725,plain,
! [X2,X3,X0,X1] :
( rS(sK25(X0,X2),X2,X0)
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(cnf_transformation,[],[f535]) ).
fof(f535,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK25(X0,X2))
& rS(sK25(X0,X2),X2,X0)
& sK25(X0,X2) != X2 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f344,f534]) ).
fof(f534,plain,
! [X0,X2] :
( ? [X4] :
( rpoint(X4)
& rS(X4,X2,X0)
& X2 != X4 )
=> ( rpoint(sK25(X0,X2))
& rS(sK25(X0,X2),X2,X0)
& sK25(X0,X2) != X2 ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& rS(X4,X2,X0)
& X2 != X4 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(flattening,[],[f343]) ).
fof(f343,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& rS(X4,X2,X0)
& X2 != X4 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(ennf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& ~ ron(X2,X0)
& X2 = X3 )
=> ? [X4] :
( rpoint(X4)
& rS(X4,X2,X0)
& X2 != X4 ) ),
inference(rectify,[],[f103]) ).
fof(f103,axiom,
! [X499,X500,X501,X502] :
( ( rline(X500)
& X499 = X500
& rpoint(X502)
& ~ ron(X501,X499)
& X501 = X502 )
=> ? [X503] :
( rpoint(X503)
& rS(X503,X501,X499)
& X501 != X503 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(33), 0), imp(cond(axiom(33), 0)))') ).
fof(f2197,plain,
spl52_117,
inference(avatar_split_clause,[],[f1054,f2195]) ).
fof(f2195,plain,
( spl52_117
<=> ! [X1,X3] :
( rpoint(vskolem1052(X1,X1,X3,X3))
| ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_117])]) ).
fof(f1054,plain,
! [X3,X1] :
( rpoint(vskolem1052(X1,X1,X3,X3))
| ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X3 ),
inference(equality_resolution,[],[f1053]) ).
fof(f1053,plain,
! [X2,X3,X1] :
( rpoint(vskolem1052(X1,X1,X2,X3))
| ~ rpoint(X1)
| ~ rpoint(X3)
| X1 = X2
| X2 != X3 ),
inference(equality_resolution,[],[f721]) ).
fof(f721,plain,
! [X2,X3,X0,X1] :
( rpoint(vskolem1052(X0,X1,X2,X3))
| ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3 ),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0,X1,X2,X3] :
( rpoint(vskolem1052(X0,X1,X2,X3))
| ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3 ),
inference(flattening,[],[f337]) ).
fof(f337,plain,
! [X0,X1,X2,X3] :
( rpoint(vskolem1052(X0,X1,X2,X3))
| ~ rpoint(X1)
| X0 != X1
| ~ rpoint(X3)
| X0 = X2
| X2 != X3 ),
inference(ennf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rpoint(X3)
& X0 != X2
& X2 = X3 )
=> rpoint(vskolem1052(X0,X1,X2,X3)) ),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X152,X153,X154,X155] :
( ( rpoint(X153)
& X152 = X153
& rpoint(X155)
& X152 != X154
& X154 = X155 )
=> rpoint(vskolem1052(X152,X153,X154,X155)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(206), 0), 2)') ).
fof(f2193,plain,
spl52_116,
inference(avatar_split_clause,[],[f1048,f2191]) ).
fof(f2191,plain,
( spl52_116
<=> ! [X1,X3] :
( rless(X3,X1)
| X1 = X3
| rless(X1,X3)
| ~ rreal(X1)
| ~ rreal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_116])]) ).
fof(f1048,plain,
! [X3,X1] :
( rless(X3,X1)
| X1 = X3
| rless(X1,X3)
| ~ rreal(X1)
| ~ rreal(X3) ),
inference(equality_resolution,[],[f1047]) ).
fof(f1047,plain,
! [X2,X3,X1] :
( rless(X2,X1)
| X1 = X2
| rless(X1,X2)
| ~ rreal(X1)
| ~ rreal(X3)
| X2 != X3 ),
inference(equality_resolution,[],[f718]) ).
fof(f718,plain,
! [X2,X3,X0,X1] :
( rless(X2,X0)
| X0 = X2
| rless(X0,X2)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0,X1,X2,X3] :
( rless(X2,X0)
| X0 = X2
| rless(X0,X2)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(flattening,[],[f333]) ).
fof(f333,plain,
! [X0,X1,X2,X3] :
( rless(X2,X0)
| X0 = X2
| rless(X0,X2)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(ennf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3 )
=> ( rless(X2,X0)
| X0 = X2
| rless(X0,X2) ) ),
inference(rectify,[],[f64]) ).
fof(f64,axiom,
! [X211,X212,X213,X214] :
( ( rreal(X212)
& X211 = X212
& rreal(X214)
& X213 = X214 )
=> ( rless(X213,X211)
| X211 = X213
| rless(X211,X213) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(145), 0), imp(cond(axiom(145), 0)))') ).
fof(f2189,plain,
spl52_115,
inference(avatar_split_clause,[],[f854,f2187]) ).
fof(f2187,plain,
( spl52_115
<=> ! [X0,X3,X2,X1] :
( rS(sK47(X0,X1,X2,X3),X1,X0)
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_115])]) ).
fof(f854,plain,
! [X2,X3,X0,X1] :
( rS(sK47(X0,X1,X2,X3),X1,X0)
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f597]) ).
fof(f597,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK47(X0,X1,X2,X3))
& rS(sK47(X0,X1,X2,X3),X1,X0)
& sK47(X0,X1,X2,X3) != X1
& sK47(X0,X1,X2,X3) != X2
& sK47(X0,X1,X2,X3) != X3 )
| ~ sP5(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f595,f596]) ).
fof(f596,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& rS(X4,X1,X0)
& X1 != X4
& X2 != X4
& X3 != X4 )
=> ( rpoint(sK47(X0,X1,X2,X3))
& rS(sK47(X0,X1,X2,X3),X1,X0)
& sK47(X0,X1,X2,X3) != X1
& sK47(X0,X1,X2,X3) != X2
& sK47(X0,X1,X2,X3) != X3 ) ),
introduced(choice_axiom,[]) ).
fof(f595,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& rS(X4,X1,X0)
& X1 != X4
& X2 != X4
& X3 != X4 )
| ~ sP5(X0,X1,X2,X3) ),
inference(rectify,[],[f594]) ).
fof(f594,plain,
! [X0,X2,X4,X6] :
( ? [X8] :
( rpoint(X8)
& rS(X8,X2,X0)
& X2 != X8
& X4 != X8
& X6 != X8 )
| ~ sP5(X0,X2,X4,X6) ),
inference(nnf_transformation,[],[f483]) ).
fof(f483,plain,
! [X0,X2,X4,X6] :
( ? [X8] :
( rpoint(X8)
& rS(X8,X2,X0)
& X2 != X8
& X4 != X8
& X6 != X8 )
| ~ sP5(X0,X2,X4,X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f2181,plain,
( ~ spl52_5
| spl52_114
| ~ spl52_16
| ~ spl52_94 ),
inference(avatar_split_clause,[],[f2171,f2086,f1653,f2179,f1602]) ).
fof(f2179,plain,
( spl52_114
<=> ! [X0] :
( ~ rpoint(X0)
| ~ ron(vd1126,sK9(X0,vd1124))
| ~ rline(sK9(X0,vd1124))
| vd1124 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_114])]) ).
fof(f2171,plain,
( ! [X0] :
( ~ rpoint(X0)
| ~ rpoint(vd1124)
| vd1124 = X0
| ~ rline(sK9(X0,vd1124))
| ~ ron(vd1126,sK9(X0,vd1124)) )
| ~ spl52_16
| ~ spl52_94 ),
inference(resolution,[],[f2087,f1654]) ).
fof(f2169,plain,
( spl52_113
| ~ spl52_5
| ~ spl52_15
| ~ spl52_93 ),
inference(avatar_split_clause,[],[f2161,f2082,f1648,f1602,f2167]) ).
fof(f1648,plain,
( spl52_15
<=> ! [X1] :
( ~ rcenter(vd1124,X1)
| ~ rcircle(X1)
| ~ ron(vd1128,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_15])]) ).
fof(f2082,plain,
( spl52_93
<=> ! [X4,X3] :
( rcenter(X3,sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_93])]) ).
fof(f2161,plain,
( ! [X0] :
( ~ rpoint(vd1124)
| ~ rpoint(X0)
| vd1124 = X0
| ~ rcircle(sK9(vd1124,X0))
| ~ ron(vd1128,sK9(vd1124,X0)) )
| ~ spl52_15
| ~ spl52_93 ),
inference(resolution,[],[f2083,f1649]) ).
fof(f1649,plain,
( ! [X1] :
( ~ rcenter(vd1124,X1)
| ~ rcircle(X1)
| ~ ron(vd1128,X1) )
| ~ spl52_15 ),
inference(avatar_component_clause,[],[f1648]) ).
fof(f2083,plain,
( ! [X3,X4] :
( rcenter(X3,sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 )
| ~ spl52_93 ),
inference(avatar_component_clause,[],[f2082]) ).
fof(f2160,plain,
spl52_112,
inference(avatar_split_clause,[],[f1105,f2158]) ).
fof(f2158,plain,
( spl52_112
<=> ! [X1,X3] :
( sK33(X1,X3) != X3
| ~ rcircle(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_112])]) ).
fof(f1105,plain,
! [X3,X1] :
( sK33(X1,X3) != X3
| ~ rcircle(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1104]) ).
fof(f1104,plain,
! [X2,X3,X1] :
( sK33(X1,X2) != X2
| ~ rcircle(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X1) ),
inference(equality_resolution,[],[f752]) ).
fof(f752,plain,
! [X2,X3,X0,X1] :
( sK33(X0,X2) != X2
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(cnf_transformation,[],[f551]) ).
fof(f551,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK33(X0,X2))
& ron(sK33(X0,X2),X0)
& sK33(X0,X2) != X2 )
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f364,f550]) ).
fof(f550,plain,
! [X0,X2] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4 )
=> ( rpoint(sK33(X0,X2))
& ron(sK33(X0,X2),X0)
& sK33(X0,X2) != X2 ) ),
introduced(choice_axiom,[]) ).
fof(f364,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4 )
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(flattening,[],[f363]) ).
fof(f363,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4 )
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(ennf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rpoint(X3)
& X2 = X3
& ron(X2,X0) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4 ) ),
inference(rectify,[],[f98]) ).
fof(f98,axiom,
! [X470,X471,X472,X473] :
( ( rcircle(X471)
& X470 = X471
& rpoint(X473)
& X472 = X473
& ron(X472,X470) )
=> ? [X474] :
( rpoint(X474)
& ron(X474,X470)
& X472 != X474 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(43), 0), imp(cond(axiom(43), 0)))') ).
fof(f2156,plain,
spl52_111,
inference(avatar_split_clause,[],[f1103,f2154]) ).
fof(f2154,plain,
( spl52_111
<=> ! [X1,X3] :
( ron(sK33(X1,X3),X1)
| ~ rcircle(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_111])]) ).
fof(f1103,plain,
! [X3,X1] :
( ron(sK33(X1,X3),X1)
| ~ rcircle(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1102]) ).
fof(f1102,plain,
! [X2,X3,X1] :
( ron(sK33(X1,X2),X1)
| ~ rcircle(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X1) ),
inference(equality_resolution,[],[f753]) ).
fof(f753,plain,
! [X2,X3,X0,X1] :
( ron(sK33(X0,X2),X0)
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(cnf_transformation,[],[f551]) ).
fof(f2152,plain,
( spl52_110
| ~ spl52_3
| ~ spl52_62 ),
inference(avatar_split_clause,[],[f1876,f1860,f1592,f2150]) ).
fof(f2150,plain,
( spl52_110
<=> ! [X0] :
( ~ rpoint(X0)
| vd684 = vg(X0,X0,vd1128) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_110])]) ).
fof(f1860,plain,
( spl52_62
<=> ! [X2,X3] :
( vd684 = vg(X2,X2,X3)
| ~ rpoint(X2)
| ~ rpoint(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_62])]) ).
fof(f1876,plain,
( ! [X0] :
( ~ rpoint(X0)
| vd684 = vg(X0,X0,vd1128) )
| ~ spl52_3
| ~ spl52_62 ),
inference(resolution,[],[f1861,f1594]) ).
fof(f1594,plain,
( rpoint(vd1128)
| ~ spl52_3 ),
inference(avatar_component_clause,[],[f1592]) ).
fof(f1861,plain,
( ! [X2,X3] :
( ~ rpoint(X3)
| ~ rpoint(X2)
| vd684 = vg(X2,X2,X3) )
| ~ spl52_62 ),
inference(avatar_component_clause,[],[f1860]) ).
fof(f2148,plain,
spl52_109,
inference(avatar_split_clause,[],[f1099,f2146]) ).
fof(f2146,plain,
( spl52_109
<=> ! [X1,X3] :
( sK32(X1,X3) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_109])]) ).
fof(f1099,plain,
! [X3,X1] :
( sK32(X1,X3) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1098]) ).
fof(f1098,plain,
! [X2,X3,X1] :
( sK32(X1,X2) != X2
| ~ rline(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X1) ),
inference(equality_resolution,[],[f749]) ).
fof(f749,plain,
! [X2,X3,X0,X1] :
( sK32(X0,X2) != X2
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(cnf_transformation,[],[f549]) ).
fof(f549,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK32(X0,X2))
& ron(sK32(X0,X2),X0)
& sK32(X0,X2) != X2 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f362,f548]) ).
fof(f548,plain,
! [X0,X2] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4 )
=> ( rpoint(sK32(X0,X2))
& ron(sK32(X0,X2),X0)
& sK32(X0,X2) != X2 ) ),
introduced(choice_axiom,[]) ).
fof(f362,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(flattening,[],[f361]) ).
fof(f361,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4 )
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(ennf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& rpoint(X3)
& X2 = X3
& ron(X2,X0) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& X2 != X4 ) ),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X563,X564,X565,X566] :
( ( rline(X564)
& X563 = X564
& rpoint(X566)
& X565 = X566
& ron(X565,X563) )
=> ? [X567] :
( rpoint(X567)
& ron(X567,X563)
& X565 != X567 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(17), 0), imp(cond(axiom(17), 0)))') ).
fof(f2144,plain,
spl52_108,
inference(avatar_split_clause,[],[f1097,f2142]) ).
fof(f2142,plain,
( spl52_108
<=> ! [X1,X3] :
( ron(sK32(X1,X3),X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_108])]) ).
fof(f1097,plain,
! [X3,X1] :
( ron(sK32(X1,X3),X1)
| ~ rline(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1096]) ).
fof(f1096,plain,
! [X2,X3,X1] :
( ron(sK32(X1,X2),X1)
| ~ rline(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X1) ),
inference(equality_resolution,[],[f750]) ).
fof(f750,plain,
! [X2,X3,X0,X1] :
( ron(sK32(X0,X2),X0)
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(cnf_transformation,[],[f549]) ).
fof(f2140,plain,
spl52_107,
inference(avatar_split_clause,[],[f1091,f2138]) ).
fof(f2138,plain,
( spl52_107
<=> ! [X1,X3] :
( ron(sK31(X1,X3),X3)
| ~ rcircle(X1)
| ~ rcircle(X3)
| ~ rintersect(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_107])]) ).
fof(f1091,plain,
! [X3,X1] :
( ron(sK31(X1,X3),X3)
| ~ rcircle(X1)
| ~ rcircle(X3)
| ~ rintersect(X1,X3) ),
inference(equality_resolution,[],[f1090]) ).
fof(f1090,plain,
! [X2,X3,X1] :
( ron(sK31(X1,X2),X2)
| ~ rcircle(X1)
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X1,X2) ),
inference(equality_resolution,[],[f745]) ).
fof(f745,plain,
! [X2,X3,X0,X1] :
( ron(sK31(X0,X2),X2)
| ~ rcircle(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f547,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK31(X0,X2))
& ron(sK31(X0,X2),X0)
& ron(sK31(X0,X2),X2) )
| ~ rcircle(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f358,f546]) ).
fof(f546,plain,
! [X0,X2] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) )
=> ( rpoint(sK31(X0,X2))
& ron(sK31(X0,X2),X0)
& ron(sK31(X0,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f358,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) )
| ~ rcircle(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(flattening,[],[f357]) ).
fof(f357,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) )
| ~ rcircle(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(ennf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rcircle(X3)
& X2 = X3
& rintersect(X0,X2) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X141,X142,X143,X144] :
( ( rcircle(X142)
& X141 = X142
& rcircle(X144)
& X143 = X144
& rintersect(X141,X143) )
=> ? [X145] :
( rpoint(X145)
& ron(X145,X141)
& ron(X145,X143) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(65), 0), imp(cond(axiom(65), 0)))') ).
fof(f2136,plain,
spl52_106,
inference(avatar_split_clause,[],[f1089,f2134]) ).
fof(f2134,plain,
( spl52_106
<=> ! [X1,X3] :
( ron(sK31(X1,X3),X1)
| ~ rcircle(X1)
| ~ rcircle(X3)
| ~ rintersect(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_106])]) ).
fof(f1089,plain,
! [X3,X1] :
( ron(sK31(X1,X3),X1)
| ~ rcircle(X1)
| ~ rcircle(X3)
| ~ rintersect(X1,X3) ),
inference(equality_resolution,[],[f1088]) ).
fof(f1088,plain,
! [X2,X3,X1] :
( ron(sK31(X1,X2),X1)
| ~ rcircle(X1)
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X1,X2) ),
inference(equality_resolution,[],[f746]) ).
fof(f746,plain,
! [X2,X3,X0,X1] :
( ron(sK31(X0,X2),X0)
| ~ rcircle(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f2132,plain,
spl52_105,
inference(avatar_split_clause,[],[f1083,f2130]) ).
fof(f2130,plain,
( spl52_105
<=> ! [X1,X3] :
( ron(sK28(X1,X3),X1)
| ~ rcircle(X1)
| ~ rline(X3)
| ~ rintersect(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_105])]) ).
fof(f1083,plain,
! [X3,X1] :
( ron(sK28(X1,X3),X1)
| ~ rcircle(X1)
| ~ rline(X3)
| ~ rintersect(X3,X1) ),
inference(equality_resolution,[],[f1082]) ).
fof(f1082,plain,
! [X2,X3,X1] :
( ron(sK28(X1,X2),X1)
| ~ rcircle(X1)
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X1) ),
inference(equality_resolution,[],[f734]) ).
fof(f734,plain,
! [X2,X3,X0,X1] :
( ron(sK28(X0,X2),X0)
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(cnf_transformation,[],[f541]) ).
fof(f541,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK28(X0,X2))
& ron(sK28(X0,X2),X2)
& ron(sK28(X0,X2),X0) )
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f354,f540]) ).
fof(f540,plain,
! [X0,X2] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0) )
=> ( rpoint(sK28(X0,X2))
& ron(sK28(X0,X2),X2)
& ron(sK28(X0,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0) )
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(flattening,[],[f353]) ).
fof(f353,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0) )
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(ennf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& rintersect(X2,X0) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0) ) ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X191,X192,X193,X194] :
( ( rcircle(X192)
& X191 = X192
& rline(X194)
& X193 = X194
& rintersect(X193,X191) )
=> ? [X195] :
( rpoint(X195)
& ron(X195,X193)
& ron(X195,X191) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(57), 0), imp(cond(axiom(57), 0)))') ).
fof(f2128,plain,
spl52_104,
inference(avatar_split_clause,[],[f1081,f2126]) ).
fof(f2126,plain,
( spl52_104
<=> ! [X1,X3] :
( ron(sK28(X1,X3),X3)
| ~ rcircle(X1)
| ~ rline(X3)
| ~ rintersect(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_104])]) ).
fof(f1081,plain,
! [X3,X1] :
( ron(sK28(X1,X3),X3)
| ~ rcircle(X1)
| ~ rline(X3)
| ~ rintersect(X3,X1) ),
inference(equality_resolution,[],[f1080]) ).
fof(f1080,plain,
! [X2,X3,X1] :
( ron(sK28(X1,X2),X2)
| ~ rcircle(X1)
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X1) ),
inference(equality_resolution,[],[f735]) ).
fof(f735,plain,
! [X2,X3,X0,X1] :
( ron(sK28(X0,X2),X2)
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(cnf_transformation,[],[f541]) ).
fof(f2124,plain,
spl52_103,
inference(avatar_split_clause,[],[f1077,f2122]) ).
fof(f2122,plain,
( spl52_103
<=> ! [X1,X3] :
( ron(sK27(X1,X3),X3)
| ~ rline(X1)
| ~ rline(X3)
| ~ rintersect(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_103])]) ).
fof(f1077,plain,
! [X3,X1] :
( ron(sK27(X1,X3),X3)
| ~ rline(X1)
| ~ rline(X3)
| ~ rintersect(X1,X3) ),
inference(equality_resolution,[],[f1076]) ).
fof(f1076,plain,
! [X2,X3,X1] :
( ron(sK27(X1,X2),X2)
| ~ rline(X1)
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X1,X2) ),
inference(equality_resolution,[],[f731]) ).
fof(f731,plain,
! [X2,X3,X0,X1] :
( ron(sK27(X0,X2),X2)
| ~ rline(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(cnf_transformation,[],[f539]) ).
fof(f539,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK27(X0,X2))
& ron(sK27(X0,X2),X0)
& ron(sK27(X0,X2),X2) )
| ~ rline(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f352,f538]) ).
fof(f538,plain,
! [X0,X2] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) )
=> ( rpoint(sK27(X0,X2))
& ron(sK27(X0,X2),X0)
& ron(sK27(X0,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f352,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) )
| ~ rline(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(flattening,[],[f351]) ).
fof(f351,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) )
| ~ rline(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(ennf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0,X1,X2,X3] :
( ( rline(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& rintersect(X0,X2) )
=> ? [X4] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X2) ) ),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X455,X456,X457,X458] :
( ( rline(X456)
& X455 = X456
& rline(X458)
& X457 = X458
& rintersect(X455,X457) )
=> ? [X459] :
( rpoint(X459)
& ron(X459,X455)
& ron(X459,X457) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(55), 0), imp(cond(axiom(55), 0)))') ).
fof(f2120,plain,
spl52_102,
inference(avatar_split_clause,[],[f1075,f2118]) ).
fof(f2118,plain,
( spl52_102
<=> ! [X1,X3] :
( ron(sK27(X1,X3),X1)
| ~ rline(X1)
| ~ rline(X3)
| ~ rintersect(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_102])]) ).
fof(f1075,plain,
! [X3,X1] :
( ron(sK27(X1,X3),X1)
| ~ rline(X1)
| ~ rline(X3)
| ~ rintersect(X1,X3) ),
inference(equality_resolution,[],[f1074]) ).
fof(f1074,plain,
! [X2,X3,X1] :
( ron(sK27(X1,X2),X1)
| ~ rline(X1)
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X1,X2) ),
inference(equality_resolution,[],[f732]) ).
fof(f732,plain,
! [X2,X3,X0,X1] :
( ron(sK27(X0,X2),X0)
| ~ rline(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(cnf_transformation,[],[f539]) ).
fof(f2116,plain,
spl52_101,
inference(avatar_split_clause,[],[f1064,f2114]) ).
fof(f2114,plain,
( spl52_101
<=> ! [X1,X3] :
( sK25(X1,X3) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_101])]) ).
fof(f1064,plain,
! [X3,X1] :
( sK25(X1,X3) != X3
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ),
inference(equality_resolution,[],[f1063]) ).
fof(f1063,plain,
! [X2,X3,X1] :
( sK25(X1,X2) != X2
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f724]) ).
fof(f724,plain,
! [X2,X3,X0,X1] :
( sK25(X0,X2) != X2
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(cnf_transformation,[],[f535]) ).
fof(f2112,plain,
spl52_100,
inference(avatar_split_clause,[],[f1016,f2110]) ).
fof(f2110,plain,
( spl52_100
<=> ! [X6,X4,X5] :
( sK20(X4,X5,X6) != X6
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_100])]) ).
fof(f1016,plain,
! [X6,X4,X5] :
( sK20(X4,X5,X6) != X6
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ),
inference(equality_resolution,[],[f1015]) ).
fof(f1015,plain,
! [X2,X6,X4,X5] :
( sK20(X4,X5,X2) != X2
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f1014]) ).
fof(f1014,plain,
! [X2,X1,X6,X4,X5] :
( sK20(X4,X1,X2) != X2
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f704]) ).
fof(f704,plain,
! [X2,X0,X1,X6,X4,X5] :
( sK20(X0,X1,X2) != X2
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(cnf_transformation,[],[f522]) ).
fof(f522,plain,
! [X0,X1,X2] :
( ( rpoint(sK20(X0,X1,X2))
& sK20(X0,X1,X2) != X0
& sK20(X0,X1,X2) != X1
& sK20(X0,X1,X2) != X2 )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f520,f521]) ).
fof(f521,plain,
! [X0,X1,X2] :
( ? [X3] :
( rpoint(X3)
& X0 != X3
& X1 != X3
& X2 != X3 )
=> ( rpoint(sK20(X0,X1,X2))
& sK20(X0,X1,X2) != X0
& sK20(X0,X1,X2) != X1
& sK20(X0,X1,X2) != X2 ) ),
introduced(choice_axiom,[]) ).
fof(f520,plain,
! [X0,X1,X2] :
( ? [X3] :
( rpoint(X3)
& X0 != X3
& X1 != X3
& X2 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X0 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X1 != X5 )
| ! [X6] :
( ~ rpoint(X6)
| X2 != X6 ) ),
inference(rectify,[],[f320]) ).
fof(f320,plain,
! [X0,X1,X2] :
( ? [X6] :
( rpoint(X6)
& X0 != X6
& X1 != X6
& X2 != X6 )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 ) ),
inference(flattening,[],[f319]) ).
fof(f319,plain,
! [X0,X1,X2] :
( ? [X6] :
( rpoint(X6)
& X0 != X6
& X1 != X6
& X2 != X6 )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| ! [X5] :
( ~ rpoint(X5)
| X2 != X5 ) ),
inference(ennf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( rpoint(X3)
& X0 = X3 )
& ? [X4] :
( rpoint(X4)
& X1 = X4 )
& ? [X5] :
( rpoint(X5)
& X2 = X5 ) )
=> ? [X6] :
( rpoint(X6)
& X0 != X6
& X1 != X6
& X2 != X6 ) ),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X580,X581,X582] :
( ( ? [X585] :
( rpoint(X585)
& X580 = X585 )
& ? [X584] :
( rpoint(X584)
& X581 = X584 )
& ? [X583] :
( rpoint(X583)
& X582 = X583 ) )
=> ? [X586] :
( rpoint(X586)
& X580 != X586
& X581 != X586
& X582 != X586 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(11), 0), imp(cond(axiom(11), 0)))') ).
fof(f2108,plain,
spl52_99,
inference(avatar_split_clause,[],[f1013,f2106]) ).
fof(f2106,plain,
( spl52_99
<=> ! [X6,X4,X5] :
( sK20(X4,X5,X6) != X5
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_99])]) ).
fof(f1013,plain,
! [X6,X4,X5] :
( sK20(X4,X5,X6) != X5
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ),
inference(equality_resolution,[],[f1012]) ).
fof(f1012,plain,
! [X2,X6,X4,X5] :
( sK20(X4,X5,X2) != X5
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f1011]) ).
fof(f1011,plain,
! [X2,X1,X6,X4,X5] :
( sK20(X4,X1,X2) != X1
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f705]) ).
fof(f705,plain,
! [X2,X0,X1,X6,X4,X5] :
( sK20(X0,X1,X2) != X1
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(cnf_transformation,[],[f522]) ).
fof(f2104,plain,
spl52_98,
inference(avatar_split_clause,[],[f1010,f2102]) ).
fof(f2102,plain,
( spl52_98
<=> ! [X6,X4,X5] :
( sK20(X4,X5,X6) != X4
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_98])]) ).
fof(f1010,plain,
! [X6,X4,X5] :
( sK20(X4,X5,X6) != X4
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ),
inference(equality_resolution,[],[f1009]) ).
fof(f1009,plain,
! [X2,X6,X4,X5] :
( sK20(X4,X5,X2) != X4
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f1008]) ).
fof(f1008,plain,
! [X2,X1,X6,X4,X5] :
( sK20(X4,X1,X2) != X4
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f706]) ).
fof(f706,plain,
! [X2,X0,X1,X6,X4,X5] :
( sK20(X0,X1,X2) != X0
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(cnf_transformation,[],[f522]) ).
fof(f2100,plain,
spl52_97,
inference(avatar_split_clause,[],[f968,f2098]) ).
fof(f2098,plain,
( spl52_97
<=> ! [X2,X3] :
( X2 = X3
| vd684 != vf(X2,X3)
| ~ rpoint(X2)
| ~ rpoint(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_97])]) ).
fof(f968,plain,
! [X2,X3] :
( X2 = X3
| vd684 != vf(X2,X3)
| ~ rpoint(X2)
| ~ rpoint(X3) ),
inference(equality_resolution,[],[f967]) ).
fof(f967,plain,
! [X2,X3,X1] :
( X1 = X2
| vd684 != vf(X2,X1)
| ~ rpoint(X2)
| ~ rpoint(X3)
| X1 != X3 ),
inference(equality_resolution,[],[f921]) ).
fof(f921,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| vd684 != vf(X0,X1)
| ~ rpoint(X2)
| X0 != X2
| ~ rpoint(X3)
| X1 != X3 ),
inference(definition_unfolding,[],[f689,f609]) ).
fof(f609,plain,
v0 = vd684,
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
v0 = vd684,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(137), 2)') ).
fof(f689,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| v0 != vf(X0,X1)
| ~ rpoint(X2)
| X0 != X2
| ~ rpoint(X3)
| X1 != X3 ),
inference(cnf_transformation,[],[f513]) ).
fof(f513,plain,
! [X0,X1] :
( ( ( v0 = vf(X0,X1)
| X0 != X1 )
& ( X0 = X1
| v0 != vf(X0,X1) ) )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(nnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0,X1] :
( ( v0 = vf(X0,X1)
<=> X0 = X1 )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(flattening,[],[f305]) ).
fof(f305,plain,
! [X0,X1] :
( ( v0 = vf(X0,X1)
<=> X0 = X1 )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(ennf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0,X1] :
( ( ? [X2] :
( rpoint(X2)
& X0 = X2 )
& ? [X3] :
( rpoint(X3)
& X1 = X3 ) )
=> ( v0 = vf(X0,X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X94,X95] :
( ( ? [X97] :
( rpoint(X97)
& X94 = X97 )
& ? [X96] :
( rpoint(X96)
& X95 = X96 ) )
=> ( v0 = vf(X94,X95)
<=> X94 = X95 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))') ).
fof(f2096,plain,
spl52_96,
inference(avatar_split_clause,[],[f944,f2094]) ).
fof(f944,plain,
! [X3,X4] :
( ron(X4,sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ),
inference(equality_resolution,[],[f943]) ).
fof(f943,plain,
! [X3,X1,X4] :
( ron(X1,sK10(X3,X1))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| X1 = X3 ),
inference(equality_resolution,[],[f663]) ).
fof(f663,plain,
! [X3,X0,X1,X4] :
( ron(X1,sK10(X0,X1))
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| X0 = X1 ),
inference(cnf_transformation,[],[f498]) ).
fof(f498,plain,
! [X0,X1] :
( ( rline(sK10(X0,X1))
& ron(X0,sK10(X0,X1))
& ron(X1,sK10(X0,X1)) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f496,f497]) ).
fof(f497,plain,
! [X0,X1] :
( ? [X2] :
( rline(X2)
& ron(X0,X2)
& ron(X1,X2) )
=> ( rline(sK10(X0,X1))
& ron(X0,sK10(X0,X1))
& ron(X1,sK10(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f496,plain,
! [X0,X1] :
( ? [X2] :
( rline(X2)
& ron(X0,X2)
& ron(X1,X2) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| X0 = X1 ),
inference(rectify,[],[f284]) ).
fof(f284,plain,
! [X0,X1] :
( ? [X4] :
( rline(X4)
& ron(X0,X4)
& ron(X1,X4) )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 )
| X0 = X1 ),
inference(flattening,[],[f283]) ).
fof(f283,plain,
! [X0,X1] :
( ? [X4] :
( rline(X4)
& ron(X0,X4)
& ron(X1,X4) )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 )
| X0 = X1 ),
inference(ennf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( ( ? [X2] :
( rpoint(X2)
& X0 = X2 )
& ? [X3] :
( rpoint(X3)
& X1 = X3 )
& X0 != X1 )
=> ? [X4] :
( rline(X4)
& ron(X0,X4)
& ron(X1,X4) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X52,X53] :
( ( ? [X55] :
( rpoint(X55)
& X52 = X55 )
& ? [X54] :
( rpoint(X54)
& X53 = X54 )
& X52 != X53 )
=> ? [X56] :
( rline(X56)
& ron(X52,X56)
& ron(X53,X56) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))') ).
fof(f2092,plain,
spl52_95,
inference(avatar_split_clause,[],[f942,f2090]) ).
fof(f942,plain,
! [X3,X4] :
( ron(X3,sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ),
inference(equality_resolution,[],[f941]) ).
fof(f941,plain,
! [X3,X1,X4] :
( ron(X3,sK10(X3,X1))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| X1 = X3 ),
inference(equality_resolution,[],[f664]) ).
fof(f664,plain,
! [X3,X0,X1,X4] :
( ron(X0,sK10(X0,X1))
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| X0 = X1 ),
inference(cnf_transformation,[],[f498]) ).
fof(f2088,plain,
spl52_94,
inference(avatar_split_clause,[],[f938,f2086]) ).
fof(f938,plain,
! [X3,X4] :
( ron(X4,sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ),
inference(equality_resolution,[],[f937]) ).
fof(f937,plain,
! [X3,X1,X4] :
( ron(X1,sK9(X3,X1))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| X1 = X3 ),
inference(equality_resolution,[],[f660]) ).
fof(f660,plain,
! [X3,X0,X1,X4] :
( ron(X1,sK9(X0,X1))
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| X0 = X1 ),
inference(cnf_transformation,[],[f495]) ).
fof(f495,plain,
! [X0,X1] :
( ( rcircle(sK9(X0,X1))
& rcenter(X0,sK9(X0,X1))
& ron(X1,sK9(X0,X1)) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f493,f494]) ).
fof(f494,plain,
! [X0,X1] :
( ? [X2] :
( rcircle(X2)
& rcenter(X0,X2)
& ron(X1,X2) )
=> ( rcircle(sK9(X0,X1))
& rcenter(X0,sK9(X0,X1))
& ron(X1,sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f493,plain,
! [X0,X1] :
( ? [X2] :
( rcircle(X2)
& rcenter(X0,X2)
& ron(X1,X2) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 )
| X0 = X1 ),
inference(rectify,[],[f282]) ).
fof(f282,plain,
! [X0,X1] :
( ? [X4] :
( rcircle(X4)
& rcenter(X0,X4)
& ron(X1,X4) )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 )
| X0 = X1 ),
inference(flattening,[],[f281]) ).
fof(f281,plain,
! [X0,X1] :
( ? [X4] :
( rcircle(X4)
& rcenter(X0,X4)
& ron(X1,X4) )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 )
| X0 = X1 ),
inference(ennf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( ( ? [X2] :
( rpoint(X2)
& X0 = X2 )
& ? [X3] :
( rpoint(X3)
& X1 = X3 )
& X0 != X1 )
=> ? [X4] :
( rcircle(X4)
& rcenter(X0,X4)
& ron(X1,X4) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X38,X39] :
( ( ? [X41] :
( rpoint(X41)
& X38 = X41 )
& ? [X40] :
( rpoint(X40)
& X39 = X40 )
& X38 != X39 )
=> ? [X42] :
( rcircle(X42)
& rcenter(X38,X42)
& ron(X39,X42) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).
fof(f2084,plain,
spl52_93,
inference(avatar_split_clause,[],[f936,f2082]) ).
fof(f936,plain,
! [X3,X4] :
( rcenter(X3,sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ),
inference(equality_resolution,[],[f935]) ).
fof(f935,plain,
! [X3,X1,X4] :
( rcenter(X3,sK9(X3,X1))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| X1 = X3 ),
inference(equality_resolution,[],[f661]) ).
fof(f661,plain,
! [X3,X0,X1,X4] :
( rcenter(X0,sK9(X0,X1))
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| X0 = X1 ),
inference(cnf_transformation,[],[f495]) ).
fof(f2080,plain,
spl52_92,
inference(avatar_split_clause,[],[f853,f2078]) ).
fof(f2078,plain,
( spl52_92
<=> ! [X0,X3,X2,X1] :
( sK47(X0,X1,X2,X3) != X1
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_92])]) ).
fof(f853,plain,
! [X2,X3,X0,X1] :
( sK47(X0,X1,X2,X3) != X1
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f597]) ).
fof(f2076,plain,
spl52_91,
inference(avatar_split_clause,[],[f852,f2074]) ).
fof(f2074,plain,
( spl52_91
<=> ! [X0,X3,X2,X1] :
( sK47(X0,X1,X2,X3) != X2
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_91])]) ).
fof(f852,plain,
! [X2,X3,X0,X1] :
( sK47(X0,X1,X2,X3) != X2
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f597]) ).
fof(f2072,plain,
spl52_90,
inference(avatar_split_clause,[],[f851,f2070]) ).
fof(f2070,plain,
( spl52_90
<=> ! [X0,X3,X2,X1] :
( sK47(X0,X1,X2,X3) != X3
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_90])]) ).
fof(f851,plain,
! [X2,X3,X0,X1] :
( sK47(X0,X1,X2,X3) != X3
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f597]) ).
fof(f2068,plain,
spl52_89,
inference(avatar_split_clause,[],[f775,f2066]) ).
fof(f2066,plain,
( spl52_89
<=> ! [X0,X3,X2,X1] :
( sK37(X0,X1,X2,X3) != X0
| ~ sP4(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_89])]) ).
fof(f775,plain,
! [X2,X3,X0,X1] :
( sK37(X0,X1,X2,X3) != X0
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f563]) ).
fof(f563,plain,
! [X0,X1,X2,X3] :
( ( rpoint(sK37(X0,X1,X2,X3))
& sK37(X0,X1,X2,X3) != X0
& sK37(X0,X1,X2,X3) != X1
& sK37(X0,X1,X2,X3) != X2
& sK37(X0,X1,X2,X3) != X3 )
| ~ sP4(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f561,f562]) ).
fof(f562,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& X0 != X4
& X1 != X4
& X2 != X4
& X3 != X4 )
=> ( rpoint(sK37(X0,X1,X2,X3))
& sK37(X0,X1,X2,X3) != X0
& sK37(X0,X1,X2,X3) != X1
& sK37(X0,X1,X2,X3) != X2
& sK37(X0,X1,X2,X3) != X3 ) ),
introduced(choice_axiom,[]) ).
fof(f561,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rpoint(X4)
& X0 != X4
& X1 != X4
& X2 != X4
& X3 != X4 )
| ~ sP4(X0,X1,X2,X3) ),
inference(rectify,[],[f560]) ).
fof(f560,plain,
! [X0,X1,X2,X3] :
( ? [X8] :
( rpoint(X8)
& X0 != X8
& X1 != X8
& X2 != X8
& X3 != X8 )
| ~ sP4(X0,X1,X2,X3) ),
inference(nnf_transformation,[],[f481]) ).
fof(f2064,plain,
spl52_88,
inference(avatar_split_clause,[],[f774,f2062]) ).
fof(f2062,plain,
( spl52_88
<=> ! [X0,X3,X2,X1] :
( sK37(X0,X1,X2,X3) != X1
| ~ sP4(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_88])]) ).
fof(f774,plain,
! [X2,X3,X0,X1] :
( sK37(X0,X1,X2,X3) != X1
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f563]) ).
fof(f2060,plain,
spl52_87,
inference(avatar_split_clause,[],[f773,f2058]) ).
fof(f2058,plain,
( spl52_87
<=> ! [X0,X3,X2,X1] :
( sK37(X0,X1,X2,X3) != X2
| ~ sP4(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_87])]) ).
fof(f773,plain,
! [X2,X3,X0,X1] :
( sK37(X0,X1,X2,X3) != X2
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f563]) ).
fof(f2056,plain,
spl52_86,
inference(avatar_split_clause,[],[f772,f2054]) ).
fof(f2054,plain,
( spl52_86
<=> ! [X0,X3,X2,X1] :
( sK37(X0,X1,X2,X3) != X3
| ~ sP4(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_86])]) ).
fof(f772,plain,
! [X2,X3,X0,X1] :
( sK37(X0,X1,X2,X3) != X3
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f563]) ).
fof(f1973,plain,
spl52_85,
inference(avatar_split_clause,[],[f1101,f1971]) ).
fof(f1971,plain,
( spl52_85
<=> ! [X1,X3] :
( rpoint(sK33(X1,X3))
| ~ rcircle(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_85])]) ).
fof(f1101,plain,
! [X3,X1] :
( rpoint(sK33(X1,X3))
| ~ rcircle(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1100]) ).
fof(f1100,plain,
! [X2,X3,X1] :
( rpoint(sK33(X1,X2))
| ~ rcircle(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X1) ),
inference(equality_resolution,[],[f754]) ).
fof(f754,plain,
! [X2,X3,X0,X1] :
( rpoint(sK33(X0,X2))
| ~ rcircle(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(cnf_transformation,[],[f551]) ).
fof(f1969,plain,
spl52_84,
inference(avatar_split_clause,[],[f1095,f1967]) ).
fof(f1967,plain,
( spl52_84
<=> ! [X1,X3] :
( rpoint(sK32(X1,X3))
| ~ rline(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_84])]) ).
fof(f1095,plain,
! [X3,X1] :
( rpoint(sK32(X1,X3))
| ~ rline(X1)
| ~ rpoint(X3)
| ~ ron(X3,X1) ),
inference(equality_resolution,[],[f1094]) ).
fof(f1094,plain,
! [X2,X3,X1] :
( rpoint(sK32(X1,X2))
| ~ rline(X1)
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X1) ),
inference(equality_resolution,[],[f751]) ).
fof(f751,plain,
! [X2,X3,X0,X1] :
( rpoint(sK32(X0,X2))
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| X2 != X3
| ~ ron(X2,X0) ),
inference(cnf_transformation,[],[f549]) ).
fof(f1965,plain,
spl52_83,
inference(avatar_split_clause,[],[f1087,f1963]) ).
fof(f1963,plain,
( spl52_83
<=> ! [X1,X3] :
( rpoint(sK31(X1,X3))
| ~ rcircle(X1)
| ~ rcircle(X3)
| ~ rintersect(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_83])]) ).
fof(f1087,plain,
! [X3,X1] :
( rpoint(sK31(X1,X3))
| ~ rcircle(X1)
| ~ rcircle(X3)
| ~ rintersect(X1,X3) ),
inference(equality_resolution,[],[f1086]) ).
fof(f1086,plain,
! [X2,X3,X1] :
( rpoint(sK31(X1,X2))
| ~ rcircle(X1)
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X1,X2) ),
inference(equality_resolution,[],[f747]) ).
fof(f747,plain,
! [X2,X3,X0,X1] :
( rpoint(sK31(X0,X2))
| ~ rcircle(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(cnf_transformation,[],[f547]) ).
fof(f1961,plain,
spl52_82,
inference(avatar_split_clause,[],[f1079,f1959]) ).
fof(f1959,plain,
( spl52_82
<=> ! [X1,X3] :
( rpoint(sK28(X1,X3))
| ~ rcircle(X1)
| ~ rline(X3)
| ~ rintersect(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_82])]) ).
fof(f1079,plain,
! [X3,X1] :
( rpoint(sK28(X1,X3))
| ~ rcircle(X1)
| ~ rline(X3)
| ~ rintersect(X3,X1) ),
inference(equality_resolution,[],[f1078]) ).
fof(f1078,plain,
! [X2,X3,X1] :
( rpoint(sK28(X1,X2))
| ~ rcircle(X1)
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X1) ),
inference(equality_resolution,[],[f736]) ).
fof(f736,plain,
! [X2,X3,X0,X1] :
( rpoint(sK28(X0,X2))
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(cnf_transformation,[],[f541]) ).
fof(f1957,plain,
spl52_81,
inference(avatar_split_clause,[],[f1073,f1955]) ).
fof(f1955,plain,
( spl52_81
<=> ! [X1,X3] :
( rpoint(sK27(X1,X3))
| ~ rline(X1)
| ~ rline(X3)
| ~ rintersect(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_81])]) ).
fof(f1073,plain,
! [X3,X1] :
( rpoint(sK27(X1,X3))
| ~ rline(X1)
| ~ rline(X3)
| ~ rintersect(X1,X3) ),
inference(equality_resolution,[],[f1072]) ).
fof(f1072,plain,
! [X2,X3,X1] :
( rpoint(sK27(X1,X2))
| ~ rline(X1)
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X1,X2) ),
inference(equality_resolution,[],[f733]) ).
fof(f733,plain,
! [X2,X3,X0,X1] :
( rpoint(sK27(X0,X2))
| ~ rline(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X0,X2) ),
inference(cnf_transformation,[],[f539]) ).
fof(f1953,plain,
spl52_80,
inference(avatar_split_clause,[],[f1069,f1951]) ).
fof(f1951,plain,
( spl52_80
<=> ! [X2,X1,X3] :
( X2 = X3
| ~ rcircle(X1)
| ~ rcenter(X2,X1)
| ~ rcenter(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_80])]) ).
fof(f1069,plain,
! [X2,X3,X1] :
( X2 = X3
| ~ rcircle(X1)
| ~ rcenter(X2,X1)
| ~ rcenter(X3,X1) ),
inference(equality_resolution,[],[f729]) ).
fof(f729,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ rcircle(X1)
| X0 != X1
| ~ rcenter(X2,X0)
| ~ rcenter(X3,X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ rcircle(X1)
| X0 != X1
| ~ rcenter(X2,X0)
| ~ rcenter(X3,X0) ),
inference(flattening,[],[f347]) ).
fof(f347,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ rcircle(X1)
| X0 != X1
| ~ rcenter(X2,X0)
| ~ rcenter(X3,X0) ),
inference(ennf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rcenter(X2,X0)
& rcenter(X3,X0) )
=> X2 = X3 ),
inference(rectify,[],[f58]) ).
fof(f58,axiom,
! [X178,X179,X180,X181] :
( ( rcircle(X179)
& X178 = X179
& rcenter(X180,X178)
& rcenter(X181,X178) )
=> X180 = X181 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(75), 0), imp(cond(axiom(75), 0)))') ).
fof(f1949,plain,
spl52_79,
inference(avatar_split_clause,[],[f1066,f1947]) ).
fof(f1947,plain,
( spl52_79
<=> ! [X1,X3] :
( rpoint(sK26(X1,X3))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_79])]) ).
fof(f1066,plain,
! [X3,X1] :
( rpoint(sK26(X1,X3))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ),
inference(equality_resolution,[],[f1065]) ).
fof(f1065,plain,
! [X2,X3,X1] :
( rpoint(sK26(X1,X2))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f728]) ).
fof(f728,plain,
! [X2,X3,X0,X1] :
( rpoint(sK26(X0,X2))
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(cnf_transformation,[],[f537]) ).
fof(f1945,plain,
spl52_78,
inference(avatar_split_clause,[],[f1060,f1943]) ).
fof(f1943,plain,
( spl52_78
<=> ! [X1,X3] :
( rpoint(sK25(X1,X3))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_78])]) ).
fof(f1060,plain,
! [X3,X1] :
( rpoint(sK25(X1,X3))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X3,X1) ),
inference(equality_resolution,[],[f1059]) ).
fof(f1059,plain,
! [X2,X3,X1] :
( rpoint(sK25(X1,X2))
| ~ rline(X1)
| ~ rpoint(X3)
| ron(X2,X1)
| X2 != X3 ),
inference(equality_resolution,[],[f726]) ).
fof(f726,plain,
! [X2,X3,X0,X1] :
( rpoint(sK25(X0,X2))
| ~ rline(X1)
| X0 != X1
| ~ rpoint(X3)
| ron(X2,X0)
| X2 != X3 ),
inference(cnf_transformation,[],[f535]) ).
fof(f1941,plain,
spl52_77,
inference(avatar_split_clause,[],[f1052,f1939]) ).
fof(f1939,plain,
( spl52_77
<=> ! [X1,X3] :
( vplus(X1,X3) = sK24(X1,X3)
| ~ rreal(X1)
| ~ rreal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_77])]) ).
fof(f1052,plain,
! [X3,X1] :
( vplus(X1,X3) = sK24(X1,X3)
| ~ rreal(X1)
| ~ rreal(X3) ),
inference(equality_resolution,[],[f1051]) ).
fof(f1051,plain,
! [X2,X3,X1] :
( vplus(X1,X2) = sK24(X1,X2)
| ~ rreal(X1)
| ~ rreal(X3)
| X2 != X3 ),
inference(equality_resolution,[],[f719]) ).
fof(f719,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) = sK24(X0,X2)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(cnf_transformation,[],[f533]) ).
fof(f533,plain,
! [X0,X1,X2,X3] :
( ( rreal(sK24(X0,X2))
& vplus(X0,X2) = sK24(X0,X2) )
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f336,f532]) ).
fof(f532,plain,
! [X0,X2] :
( ? [X4] :
( rreal(X4)
& vplus(X0,X2) = X4 )
=> ( rreal(sK24(X0,X2))
& vplus(X0,X2) = sK24(X0,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rreal(X4)
& vplus(X0,X2) = X4 )
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(flattening,[],[f335]) ).
fof(f335,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( rreal(X4)
& vplus(X0,X2) = X4 )
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(ennf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1,X2,X3] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3 )
=> ? [X4] :
( rreal(X4)
& vplus(X0,X2) = X4 ) ),
inference(rectify,[],[f66]) ).
fof(f66,axiom,
! [X219,X220,X221,X222] :
( ( rreal(X220)
& X219 = X220
& rreal(X222)
& X221 = X222 )
=> ? [X223] :
( rreal(X223)
& vplus(X219,X221) = X223 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(139), 0), imp(cond(axiom(139), 0)))') ).
fof(f1937,plain,
spl52_76,
inference(avatar_split_clause,[],[f1046,f1935]) ).
fof(f1935,plain,
( spl52_76
<=> ! [X1,X3] :
( vplus(X1,X3) = vplus(X3,X1)
| ~ rreal(X1)
| ~ rreal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_76])]) ).
fof(f1046,plain,
! [X3,X1] :
( vplus(X1,X3) = vplus(X3,X1)
| ~ rreal(X1)
| ~ rreal(X3) ),
inference(equality_resolution,[],[f1045]) ).
fof(f1045,plain,
! [X2,X3,X1] :
( vplus(X1,X2) = vplus(X2,X1)
| ~ rreal(X1)
| ~ rreal(X3)
| X2 != X3 ),
inference(equality_resolution,[],[f717]) ).
fof(f717,plain,
! [X2,X3,X0,X1] :
( vplus(X0,X2) = vplus(X2,X0)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(cnf_transformation,[],[f332]) ).
fof(f332,plain,
! [X0,X1,X2,X3] :
( vplus(X0,X2) = vplus(X2,X0)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(flattening,[],[f331]) ).
fof(f331,plain,
! [X0,X1,X2,X3] :
( vplus(X0,X2) = vplus(X2,X0)
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(ennf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( ( rreal(X1)
& X0 = X1
& rreal(X3)
& X2 = X3 )
=> vplus(X0,X2) = vplus(X2,X0) ),
inference(rectify,[],[f65]) ).
fof(f65,axiom,
! [X215,X216,X217,X218] :
( ( rreal(X216)
& X215 = X216
& rreal(X218)
& X217 = X218 )
=> vplus(X215,X217) = vplus(X217,X215) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(143), 0), imp(cond(axiom(143), 0)))') ).
fof(f1933,plain,
spl52_75,
inference(avatar_split_clause,[],[f1044,f1931]) ).
fof(f1931,plain,
( spl52_75
<=> ! [X1,X3] :
( rS(X1,X1,X3)
| ~ rpoint(X1)
| ~ rline(X3)
| ron(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_75])]) ).
fof(f1044,plain,
! [X3,X1] :
( rS(X1,X1,X3)
| ~ rpoint(X1)
| ~ rline(X3)
| ron(X1,X3) ),
inference(equality_resolution,[],[f1043]) ).
fof(f1043,plain,
! [X2,X3,X1] :
( rS(X1,X1,X2)
| ~ rpoint(X1)
| ~ rline(X3)
| X2 != X3
| ron(X1,X2) ),
inference(equality_resolution,[],[f716]) ).
fof(f716,plain,
! [X2,X3,X0,X1] :
( rS(X0,X0,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ron(X0,X2) ),
inference(cnf_transformation,[],[f330]) ).
fof(f330,plain,
! [X0,X1,X2,X3] :
( rS(X0,X0,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ron(X0,X2) ),
inference(flattening,[],[f329]) ).
fof(f329,plain,
! [X0,X1,X2,X3] :
( rS(X0,X0,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ron(X0,X2) ),
inference(ennf_transformation,[],[f163]) ).
fof(f163,plain,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& ~ ron(X0,X2) )
=> rS(X0,X0,X2) ),
inference(rectify,[],[f85]) ).
fof(f85,axiom,
! [X377,X378,X379,X380] :
( ( rpoint(X378)
& X377 = X378
& rline(X380)
& X379 = X380
& ~ ron(X377,X379) )
=> rS(X377,X377,X379) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(95), 0), imp(cond(axiom(95), 0)))') ).
fof(f1929,plain,
spl52_74,
inference(avatar_split_clause,[],[f1019,f1927]) ).
fof(f1927,plain,
( spl52_74
<=> ! [X6,X4,X5] :
( rreal(sK21(X4,X5,X6))
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_74])]) ).
fof(f1019,plain,
! [X6,X4,X5] :
( rreal(sK21(X4,X5,X6))
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ),
inference(equality_resolution,[],[f1018]) ).
fof(f1018,plain,
! [X2,X6,X4,X5] :
( rreal(sK21(X4,X5,X2))
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f1017]) ).
fof(f1017,plain,
! [X2,X1,X6,X4,X5] :
( rreal(sK21(X4,X1,X2))
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f709]) ).
fof(f709,plain,
! [X2,X0,X1,X6,X4,X5] :
( rreal(sK21(X0,X1,X2))
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(cnf_transformation,[],[f525]) ).
fof(f1925,plain,
spl52_73,
inference(avatar_split_clause,[],[f1007,f1923]) ).
fof(f1923,plain,
( spl52_73
<=> ! [X6,X4,X5] :
( rpoint(sK20(X4,X5,X6))
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_73])]) ).
fof(f1007,plain,
! [X6,X4,X5] :
( rpoint(sK20(X4,X5,X6))
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6) ),
inference(equality_resolution,[],[f1006]) ).
fof(f1006,plain,
! [X2,X6,X4,X5] :
( rpoint(sK20(X4,X5,X2))
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f1005]) ).
fof(f1005,plain,
! [X2,X1,X6,X4,X5] :
( rpoint(sK20(X4,X1,X2))
| ~ rpoint(X4)
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(equality_resolution,[],[f707]) ).
fof(f707,plain,
! [X2,X0,X1,X6,X4,X5] :
( rpoint(sK20(X0,X1,X2))
| ~ rpoint(X4)
| X0 != X4
| ~ rpoint(X5)
| X1 != X5
| ~ rpoint(X6)
| X2 != X6 ),
inference(cnf_transformation,[],[f522]) ).
fof(f1921,plain,
spl52_72,
inference(avatar_split_clause,[],[f978,f1919]) ).
fof(f1919,plain,
( spl52_72
<=> ! [X4,X3] :
( vf(X3,X4) = sK19(X3,X4)
| ~ rpoint(X3)
| ~ rpoint(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_72])]) ).
fof(f978,plain,
! [X3,X4] :
( vf(X3,X4) = sK19(X3,X4)
| ~ rpoint(X3)
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f977]) ).
fof(f977,plain,
! [X3,X1,X4] :
( sK19(X3,X1) = vf(X3,X1)
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4 ),
inference(equality_resolution,[],[f694]) ).
fof(f694,plain,
! [X3,X0,X1,X4] :
( vf(X0,X1) = sK19(X0,X1)
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4 ),
inference(cnf_transformation,[],[f519]) ).
fof(f519,plain,
! [X0,X1] :
( ( rreal(sK19(X0,X1))
& vf(X0,X1) = sK19(X0,X1) )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f517,f518]) ).
fof(f518,plain,
! [X0,X1] :
( ? [X2] :
( rreal(X2)
& vf(X0,X1) = X2 )
=> ( rreal(sK19(X0,X1))
& vf(X0,X1) = sK19(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f517,plain,
! [X0,X1] :
( ? [X2] :
( rreal(X2)
& vf(X0,X1) = X2 )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 ) ),
inference(rectify,[],[f310]) ).
fof(f310,plain,
! [X0,X1] :
( ? [X4] :
( rreal(X4)
& vf(X0,X1) = X4 )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(flattening,[],[f309]) ).
fof(f309,plain,
! [X0,X1] :
( ? [X4] :
( rreal(X4)
& vf(X0,X1) = X4 )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(ennf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0,X1] :
( ( ? [X2] :
( rpoint(X2)
& X0 = X2 )
& ? [X3] :
( rpoint(X3)
& X1 = X3 ) )
=> ? [X4] :
( rreal(X4)
& vf(X0,X1) = X4 ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X57,X58] :
( ( ? [X60] :
( rpoint(X60)
& X57 = X60 )
& ? [X59] :
( rpoint(X59)
& X58 = X59 ) )
=> ? [X61] :
( rreal(X61)
& vf(X57,X58) = X61 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(160), 0), imp(cond(axiom(160), 0)))') ).
fof(f1917,plain,
spl52_71,
inference(avatar_split_clause,[],[f963,f1915]) ).
fof(f1915,plain,
( spl52_71
<=> ! [X2,X3] :
( vf(X3,X2) = vf(X2,X3)
| ~ rpoint(X2)
| ~ rpoint(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_71])]) ).
fof(f963,plain,
! [X2,X3] :
( vf(X3,X2) = vf(X2,X3)
| ~ rpoint(X2)
| ~ rpoint(X3) ),
inference(equality_resolution,[],[f962]) ).
fof(f962,plain,
! [X2,X3,X1] :
( vf(X1,X2) = vf(X2,X1)
| ~ rpoint(X2)
| ~ rpoint(X3)
| X1 != X3 ),
inference(equality_resolution,[],[f688]) ).
fof(f688,plain,
! [X2,X3,X0,X1] :
( vf(X0,X1) = vf(X1,X0)
| ~ rpoint(X2)
| X0 != X2
| ~ rpoint(X3)
| X1 != X3 ),
inference(cnf_transformation,[],[f304]) ).
fof(f304,plain,
! [X0,X1] :
( vf(X0,X1) = vf(X1,X0)
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(flattening,[],[f303]) ).
fof(f303,plain,
! [X0,X1] :
( vf(X0,X1) = vf(X1,X0)
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(ennf_transformation,[],[f149]) ).
fof(f149,plain,
! [X0,X1] :
( ( ? [X2] :
( rpoint(X2)
& X0 = X2 )
& ? [X3] :
( rpoint(X3)
& X1 = X3 ) )
=> vf(X0,X1) = vf(X1,X0) ),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X677,X678] :
( ( ? [X680] :
( rpoint(X680)
& X677 = X680 )
& ? [X679] :
( rpoint(X679)
& X678 = X679 ) )
=> vf(X677,X678) = vf(X678,X677) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))') ).
fof(f1913,plain,
spl52_70,
inference(avatar_split_clause,[],[f940,f1911]) ).
fof(f940,plain,
! [X3,X4] :
( rline(sK10(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ),
inference(equality_resolution,[],[f939]) ).
fof(f939,plain,
! [X3,X1,X4] :
( rline(sK10(X3,X1))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| X1 = X3 ),
inference(equality_resolution,[],[f665]) ).
fof(f665,plain,
! [X3,X0,X1,X4] :
( rline(sK10(X0,X1))
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| X0 = X1 ),
inference(cnf_transformation,[],[f498]) ).
fof(f1909,plain,
spl52_69,
inference(avatar_split_clause,[],[f934,f1907]) ).
fof(f934,plain,
! [X3,X4] :
( rcircle(sK9(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X3 = X4 ),
inference(equality_resolution,[],[f933]) ).
fof(f933,plain,
! [X3,X1,X4] :
( rcircle(sK9(X3,X1))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| X1 = X3 ),
inference(equality_resolution,[],[f662]) ).
fof(f662,plain,
! [X3,X0,X1,X4] :
( rcircle(sK9(X0,X1))
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| X0 = X1 ),
inference(cnf_transformation,[],[f495]) ).
fof(f1905,plain,
( spl52_68
| ~ spl52_2
| ~ spl52_37 ),
inference(avatar_split_clause,[],[f1750,f1738,f1587,f1902]) ).
fof(f1902,plain,
( spl52_68
<=> vd684 = vf(vd14,vd14) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_68])]) ).
fof(f1587,plain,
( spl52_2
<=> rpoint(vd14) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_2])]) ).
fof(f1738,plain,
( spl52_37
<=> ! [X3] :
( vd684 = vf(X3,X3)
| ~ rpoint(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_37])]) ).
fof(f1750,plain,
( vd684 = vf(vd14,vd14)
| ~ spl52_2
| ~ spl52_37 ),
inference(resolution,[],[f1739,f1589]) ).
fof(f1589,plain,
( rpoint(vd14)
| ~ spl52_2 ),
inference(avatar_component_clause,[],[f1587]) ).
fof(f1739,plain,
( ! [X3] :
( ~ rpoint(X3)
| vd684 = vf(X3,X3) )
| ~ spl52_37 ),
inference(avatar_component_clause,[],[f1738]) ).
fof(f1900,plain,
spl52_67,
inference(avatar_split_clause,[],[f855,f1898]) ).
fof(f1898,plain,
( spl52_67
<=> ! [X0,X3,X2,X1] :
( rpoint(sK47(X0,X1,X2,X3))
| ~ sP5(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_67])]) ).
fof(f855,plain,
! [X2,X3,X0,X1] :
( rpoint(sK47(X0,X1,X2,X3))
| ~ sP5(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f597]) ).
fof(f1896,plain,
spl52_66,
inference(avatar_split_clause,[],[f776,f1894]) ).
fof(f1894,plain,
( spl52_66
<=> ! [X0,X3,X2,X1] :
( rpoint(sK37(X0,X1,X2,X3))
| ~ sP4(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_66])]) ).
fof(f776,plain,
! [X2,X3,X0,X1] :
( rpoint(sK37(X0,X1,X2,X3))
| ~ sP4(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f563]) ).
fof(f1875,plain,
spl52_65,
inference(avatar_split_clause,[],[f1093,f1873]) ).
fof(f1873,plain,
( spl52_65
<=> ! [X1,X3] :
( ~ ron(X1,X3)
| ~ rpoint(X1)
| ~ rcircle(X3)
| ~ rinside(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_65])]) ).
fof(f1093,plain,
! [X3,X1] :
( ~ ron(X1,X3)
| ~ rpoint(X1)
| ~ rcircle(X3)
| ~ rinside(X1,X3) ),
inference(equality_resolution,[],[f1092]) ).
fof(f1092,plain,
! [X2,X3,X1] :
( ~ ron(X1,X2)
| ~ rpoint(X1)
| ~ rcircle(X3)
| X2 != X3
| ~ rinside(X1,X2) ),
inference(equality_resolution,[],[f748]) ).
fof(f748,plain,
! [X2,X3,X0,X1] :
( ~ ron(X0,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rinside(X0,X2) ),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0,X1,X2,X3] :
( ~ ron(X0,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rinside(X0,X2) ),
inference(flattening,[],[f359]) ).
fof(f359,plain,
! [X0,X1,X2,X3] :
( ~ ron(X0,X2)
| ~ rpoint(X1)
| X0 != X1
| ~ rcircle(X3)
| X2 != X3
| ~ rinside(X0,X2) ),
inference(ennf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0,X1,X2,X3] :
( ( rpoint(X1)
& X0 = X1
& rcircle(X3)
& X2 = X3
& rinside(X0,X2) )
=> ~ ron(X0,X2) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X28,X29,X30,X31] :
( ( rpoint(X29)
& X28 = X29
& rcircle(X31)
& X30 = X31
& rinside(X28,X30) )
=> ~ ron(X28,X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(79), 0), imp(cond(axiom(79), 0)))') ).
fof(f1871,plain,
spl52_64,
inference(avatar_split_clause,[],[f1085,f1869]) ).
fof(f1869,plain,
( spl52_64
<=> ! [X1,X3] :
( sP3(X3,X1)
| ~ rcircle(X1)
| ~ rline(X3)
| ~ rintersect(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_64])]) ).
fof(f1085,plain,
! [X3,X1] :
( sP3(X3,X1)
| ~ rcircle(X1)
| ~ rline(X3)
| ~ rintersect(X3,X1) ),
inference(equality_resolution,[],[f1084]) ).
fof(f1084,plain,
! [X2,X3,X1] :
( sP3(X2,X1)
| ~ rcircle(X1)
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X1) ),
inference(equality_resolution,[],[f744]) ).
fof(f744,plain,
! [X2,X3,X0,X1] :
( sP3(X2,X0)
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(cnf_transformation,[],[f480]) ).
fof(f480,plain,
! [X0,X1,X2,X3] :
( sP3(X2,X0)
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(definition_folding,[],[f356,f479]) ).
fof(f479,plain,
! [X2,X0] :
( ? [X4,X5] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0)
& rpoint(X5)
& ron(X5,X2)
& ron(X5,X0)
& X4 != X5 )
| ~ sP3(X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f356,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0)
& rpoint(X5)
& ron(X5,X2)
& ron(X5,X0)
& X4 != X5 )
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(flattening,[],[f355]) ).
fof(f355,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0)
& rpoint(X5)
& ron(X5,X2)
& ron(X5,X0)
& X4 != X5 )
| ~ rcircle(X1)
| X0 != X1
| ~ rline(X3)
| X2 != X3
| ~ rintersect(X2,X0) ),
inference(ennf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0,X1,X2,X3] :
( ( rcircle(X1)
& X0 = X1
& rline(X3)
& X2 = X3
& rintersect(X2,X0) )
=> ? [X4,X5] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0)
& rpoint(X5)
& ron(X5,X2)
& ron(X5,X0)
& X4 != X5 ) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X146,X147,X148,X149] :
( ( rcircle(X147)
& X146 = X147
& rline(X149)
& X148 = X149
& rintersect(X148,X146) )
=> ? [X150,X151] :
( rpoint(X150)
& ron(X150,X148)
& ron(X150,X146)
& rpoint(X151)
& ron(X151,X148)
& ron(X151,X146)
& X150 != X151 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(59), 0), imp(cond(axiom(59), 0)))') ).
fof(f1867,plain,
( spl52_63
| ~ spl52_5
| ~ spl52_37 ),
inference(avatar_split_clause,[],[f1749,f1738,f1602,f1864]) ).
fof(f1864,plain,
( spl52_63
<=> vd684 = vf(vd1124,vd1124) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_63])]) ).
fof(f1749,plain,
( vd684 = vf(vd1124,vd1124)
| ~ spl52_5
| ~ spl52_37 ),
inference(resolution,[],[f1739,f1604]) ).
fof(f1604,plain,
( rpoint(vd1124)
| ~ spl52_5 ),
inference(avatar_component_clause,[],[f1602]) ).
fof(f1862,plain,
spl52_62,
inference(avatar_split_clause,[],[f961,f1860]) ).
fof(f961,plain,
! [X2,X3] :
( vd684 = vg(X2,X2,X3)
| ~ rpoint(X2)
| ~ rpoint(X3) ),
inference(equality_resolution,[],[f960]) ).
fof(f960,plain,
! [X2,X3,X1] :
( vd684 = vg(X2,X2,X1)
| ~ rpoint(X2)
| ~ rpoint(X3)
| X1 != X3 ),
inference(equality_resolution,[],[f919]) ).
fof(f919,plain,
! [X2,X3,X0,X1] :
( vd684 = vg(X0,X0,X1)
| ~ rpoint(X2)
| X0 != X2
| ~ rpoint(X3)
| X1 != X3 ),
inference(definition_unfolding,[],[f687,f609]) ).
fof(f687,plain,
! [X2,X3,X0,X1] :
( v0 = vg(X0,X0,X1)
| ~ rpoint(X2)
| X0 != X2
| ~ rpoint(X3)
| X1 != X3 ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0,X1] :
( v0 = vg(X0,X0,X1)
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(flattening,[],[f301]) ).
fof(f301,plain,
! [X0,X1] :
( v0 = vg(X0,X0,X1)
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(ennf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0,X1] :
( ( ? [X2] :
( rpoint(X2)
& X0 = X2 )
& ? [X3] :
( rpoint(X3)
& X1 = X3 ) )
=> v0 = vg(X0,X0,X1) ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X718,X719] :
( ( ? [X721] :
( rpoint(X721)
& X718 = X721 )
& ? [X720] :
( rpoint(X720)
& X719 = X720 ) )
=> v0 = vg(X718,X718,X719) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(172), 0), imp(cond(axiom(172), 0)))') ).
fof(f1858,plain,
spl52_61,
inference(avatar_split_clause,[],[f959,f1856]) ).
fof(f1856,plain,
( spl52_61
<=> ! [X2,X3] :
( sP2(X2,X3)
| ~ rcircle(X2)
| ~ rcircle(X3)
| ~ rintersect(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_61])]) ).
fof(f959,plain,
! [X2,X3] :
( sP2(X2,X3)
| ~ rcircle(X2)
| ~ rcircle(X3)
| ~ rintersect(X2,X3) ),
inference(equality_resolution,[],[f958]) ).
fof(f958,plain,
! [X2,X3,X1] :
( sP2(X2,X1)
| ~ rcircle(X2)
| ~ rcircle(X3)
| X1 != X3
| ~ rintersect(X2,X1) ),
inference(equality_resolution,[],[f686]) ).
fof(f686,plain,
! [X2,X3,X0,X1] :
( sP2(X0,X1)
| ~ rcircle(X2)
| X0 != X2
| ~ rcircle(X3)
| X1 != X3
| ~ rintersect(X0,X1) ),
inference(cnf_transformation,[],[f478]) ).
fof(f478,plain,
! [X0,X1] :
( sP2(X0,X1)
| ! [X2] :
( ~ rcircle(X2)
| X0 != X2 )
| ! [X3] :
( ~ rcircle(X3)
| X1 != X3 )
| ~ rintersect(X0,X1) ),
inference(definition_folding,[],[f300,f477]) ).
fof(f477,plain,
! [X0,X1] :
( ? [X4,X5] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X1)
& rpoint(X5)
& ron(X5,X0)
& ron(X5,X1)
& X4 != X5 )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f300,plain,
! [X0,X1] :
( ? [X4,X5] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X1)
& rpoint(X5)
& ron(X5,X0)
& ron(X5,X1)
& X4 != X5 )
| ! [X2] :
( ~ rcircle(X2)
| X0 != X2 )
| ! [X3] :
( ~ rcircle(X3)
| X1 != X3 )
| ~ rintersect(X0,X1) ),
inference(flattening,[],[f299]) ).
fof(f299,plain,
! [X0,X1] :
( ? [X4,X5] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X1)
& rpoint(X5)
& ron(X5,X0)
& ron(X5,X1)
& X4 != X5 )
| ! [X2] :
( ~ rcircle(X2)
| X0 != X2 )
| ! [X3] :
( ~ rcircle(X3)
| X1 != X3 )
| ~ rintersect(X0,X1) ),
inference(ennf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0,X1] :
( ( ? [X2] :
( rcircle(X2)
& X0 = X2 )
& ? [X3] :
( rcircle(X3)
& X1 = X3 )
& rintersect(X0,X1) )
=> ? [X4,X5] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X1)
& rpoint(X5)
& ron(X5,X0)
& ron(X5,X1)
& X4 != X5 ) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X32,X33] :
( ( ? [X35] :
( rcircle(X35)
& X32 = X35 )
& ? [X34] :
( rcircle(X34)
& X33 = X34 )
& rintersect(X32,X33) )
=> ? [X36,X37] :
( rpoint(X36)
& ron(X36,X32)
& ron(X36,X33)
& rpoint(X37)
& ron(X37,X32)
& ron(X37,X33)
& X36 != X37 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(67), 0), imp(cond(axiom(67), 0)))') ).
fof(f1854,plain,
spl52_60,
inference(avatar_split_clause,[],[f737,f1852]) ).
fof(f1852,plain,
( spl52_60
<=> ! [X0,X1] :
( sK29(X0,X1) != sK30(X0,X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_60])]) ).
fof(f737,plain,
! [X0,X1] :
( sK29(X0,X1) != sK30(X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
fof(f545,plain,
! [X0,X1] :
( ( rpoint(sK29(X0,X1))
& ron(sK29(X0,X1),X0)
& ron(sK29(X0,X1),X1)
& rpoint(sK30(X0,X1))
& ron(sK30(X0,X1),X0)
& ron(sK30(X0,X1),X1)
& sK29(X0,X1) != sK30(X0,X1) )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f543,f544]) ).
fof(f544,plain,
! [X0,X1] :
( ? [X2,X3] :
( rpoint(X2)
& ron(X2,X0)
& ron(X2,X1)
& rpoint(X3)
& ron(X3,X0)
& ron(X3,X1)
& X2 != X3 )
=> ( rpoint(sK29(X0,X1))
& ron(sK29(X0,X1),X0)
& ron(sK29(X0,X1),X1)
& rpoint(sK30(X0,X1))
& ron(sK30(X0,X1),X0)
& ron(sK30(X0,X1),X1)
& sK29(X0,X1) != sK30(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f543,plain,
! [X0,X1] :
( ? [X2,X3] :
( rpoint(X2)
& ron(X2,X0)
& ron(X2,X1)
& rpoint(X3)
& ron(X3,X0)
& ron(X3,X1)
& X2 != X3 )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f542]) ).
fof(f542,plain,
! [X2,X0] :
( ? [X4,X5] :
( rpoint(X4)
& ron(X4,X2)
& ron(X4,X0)
& rpoint(X5)
& ron(X5,X2)
& ron(X5,X0)
& X4 != X5 )
| ~ sP3(X2,X0) ),
inference(nnf_transformation,[],[f479]) ).
fof(f1850,plain,
spl52_59,
inference(avatar_split_clause,[],[f679,f1848]) ).
fof(f1848,plain,
( spl52_59
<=> ! [X0,X1] :
( sK16(X0,X1) != sK17(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_59])]) ).
fof(f679,plain,
! [X0,X1] :
( sK16(X0,X1) != sK17(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f512,plain,
! [X0,X1] :
( ( rpoint(sK16(X0,X1))
& ron(sK16(X0,X1),X0)
& ron(sK16(X0,X1),X1)
& rpoint(sK17(X0,X1))
& ron(sK17(X0,X1),X0)
& ron(sK17(X0,X1),X1)
& sK16(X0,X1) != sK17(X0,X1) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f510,f511]) ).
fof(f511,plain,
! [X0,X1] :
( ? [X2,X3] :
( rpoint(X2)
& ron(X2,X0)
& ron(X2,X1)
& rpoint(X3)
& ron(X3,X0)
& ron(X3,X1)
& X2 != X3 )
=> ( rpoint(sK16(X0,X1))
& ron(sK16(X0,X1),X0)
& ron(sK16(X0,X1),X1)
& rpoint(sK17(X0,X1))
& ron(sK17(X0,X1),X0)
& ron(sK17(X0,X1),X1)
& sK16(X0,X1) != sK17(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f510,plain,
! [X0,X1] :
( ? [X2,X3] :
( rpoint(X2)
& ron(X2,X0)
& ron(X2,X1)
& rpoint(X3)
& ron(X3,X0)
& ron(X3,X1)
& X2 != X3 )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f509]) ).
fof(f509,plain,
! [X0,X1] :
( ? [X4,X5] :
( rpoint(X4)
& ron(X4,X0)
& ron(X4,X1)
& rpoint(X5)
& ron(X5,X0)
& ron(X5,X1)
& X4 != X5 )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f477]) ).
fof(f1846,plain,
spl52_58,
inference(avatar_split_clause,[],[f974,f1844]) ).
fof(f1844,plain,
( spl52_58
<=> ! [X4,X3] :
( sK18(X3,X4) != X4
| ~ rpoint(X3)
| ~ rpoint(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_58])]) ).
fof(f974,plain,
! [X3,X4] :
( sK18(X3,X4) != X4
| ~ rpoint(X3)
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f973]) ).
fof(f973,plain,
! [X3,X1,X4] :
( sK18(X3,X1) != X1
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4 ),
inference(equality_resolution,[],[f691]) ).
fof(f691,plain,
! [X3,X0,X1,X4] :
( sK18(X0,X1) != X1
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4 ),
inference(cnf_transformation,[],[f516]) ).
fof(f516,plain,
! [X0,X1] :
( ( rpoint(sK18(X0,X1))
& sK18(X0,X1) != X0
& sK18(X0,X1) != X1 )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f514,f515]) ).
fof(f515,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& X0 != X2
& X1 != X2 )
=> ( rpoint(sK18(X0,X1))
& sK18(X0,X1) != X0
& sK18(X0,X1) != X1 ) ),
introduced(choice_axiom,[]) ).
fof(f514,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& X0 != X2
& X1 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X0 != X3 )
| ! [X4] :
( ~ rpoint(X4)
| X1 != X4 ) ),
inference(rectify,[],[f308]) ).
fof(f308,plain,
! [X0,X1] :
( ? [X4] :
( rpoint(X4)
& X0 != X4
& X1 != X4 )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(flattening,[],[f307]) ).
fof(f307,plain,
! [X0,X1] :
( ? [X4] :
( rpoint(X4)
& X0 != X4
& X1 != X4 )
| ! [X2] :
( ~ rpoint(X2)
| X0 != X2 )
| ! [X3] :
( ~ rpoint(X3)
| X1 != X3 ) ),
inference(ennf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0,X1] :
( ( ? [X2] :
( rpoint(X2)
& X0 = X2 )
& ? [X3] :
( rpoint(X3)
& X1 = X3 ) )
=> ? [X4] :
( rpoint(X4)
& X0 != X4
& X1 != X4 ) ),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X587,X588] :
( ( ? [X590] :
( rpoint(X590)
& X587 = X590 )
& ? [X589] :
( rpoint(X589)
& X588 = X589 ) )
=> ? [X591] :
( rpoint(X591)
& X587 != X591
& X588 != X591 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(9), 0), imp(cond(axiom(9), 0)))') ).
fof(f1842,plain,
spl52_57,
inference(avatar_split_clause,[],[f972,f1840]) ).
fof(f1840,plain,
( spl52_57
<=> ! [X4,X3] :
( sK18(X3,X4) != X3
| ~ rpoint(X3)
| ~ rpoint(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_57])]) ).
fof(f972,plain,
! [X3,X4] :
( sK18(X3,X4) != X3
| ~ rpoint(X3)
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f971]) ).
fof(f971,plain,
! [X3,X1,X4] :
( sK18(X3,X1) != X3
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4 ),
inference(equality_resolution,[],[f692]) ).
fof(f692,plain,
! [X3,X0,X1,X4] :
( sK18(X0,X1) != X0
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4 ),
inference(cnf_transformation,[],[f516]) ).
fof(f1838,plain,
( spl52_56
| ~ spl52_4
| ~ spl52_37 ),
inference(avatar_split_clause,[],[f1748,f1738,f1597,f1835]) ).
fof(f1835,plain,
( spl52_56
<=> vd684 = vf(vd1126,vd1126) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_56])]) ).
fof(f1748,plain,
( vd684 = vf(vd1126,vd1126)
| ~ spl52_4
| ~ spl52_37 ),
inference(resolution,[],[f1739,f1599]) ).
fof(f1599,plain,
( rpoint(vd1126)
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f1597]) ).
fof(f1830,plain,
( spl52_55
| ~ spl52_3
| ~ spl52_37 ),
inference(avatar_split_clause,[],[f1747,f1738,f1592,f1827]) ).
fof(f1827,plain,
( spl52_55
<=> vd684 = vf(vd1128,vd1128) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_55])]) ).
fof(f1747,plain,
( vd684 = vf(vd1128,vd1128)
| ~ spl52_3
| ~ spl52_37 ),
inference(resolution,[],[f1739,f1594]) ).
fof(f1825,plain,
spl52_54,
inference(avatar_split_clause,[],[f1558,f1823]) ).
fof(f1823,plain,
( spl52_54
<=> ! [X4,X5] :
( ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_54])]) ).
fof(f1558,plain,
! [X4,X5] :
( ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X4,X5) ),
inference(duplicate_literal_removal,[],[f991]) ).
fof(f991,plain,
! [X4,X5] :
( ~ rpoint(X4)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X4,X5) ),
inference(equality_resolution,[],[f990]) ).
fof(f990,plain,
! [X2,X4,X5] :
( ~ rpoint(X4)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X4,X4,X2) ),
inference(equality_resolution,[],[f989]) ).
fof(f989,plain,
! [X2,X3,X4,X5] :
( ~ rpoint(X3)
| ~ rpoint(X4)
| X3 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X3,X3,X2) ),
inference(equality_resolution,[],[f988]) ).
fof(f988,plain,
! [X2,X3,X1,X4,X5] :
( ~ rpoint(X3)
| X1 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X1,X2) ),
inference(equality_resolution,[],[f700]) ).
fof(f700,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 != X1
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X0,X2) ),
inference(cnf_transformation,[],[f316]) ).
fof(f1821,plain,
spl52_53,
inference(avatar_split_clause,[],[f1557,f1819]) ).
fof(f1819,plain,
( spl52_53
<=> ! [X4,X5] :
( ~ rpoint(X5)
| ~ rpoint(X4)
| ~ rR(X4,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_53])]) ).
fof(f1557,plain,
! [X4,X5] :
( ~ rpoint(X5)
| ~ rpoint(X4)
| ~ rR(X4,X5,X5) ),
inference(duplicate_literal_removal,[],[f995]) ).
fof(f995,plain,
! [X4,X5] :
( ~ rpoint(X5)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rR(X4,X5,X5) ),
inference(equality_resolution,[],[f994]) ).
fof(f994,plain,
! [X3,X4,X5] :
( ~ rpoint(X3)
| ~ rpoint(X4)
| ~ rpoint(X5)
| X3 != X5
| ~ rR(X4,X3,X3) ),
inference(equality_resolution,[],[f993]) ).
fof(f993,plain,
! [X3,X1,X4,X5] :
( ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X3 != X5
| ~ rR(X1,X3,X3) ),
inference(equality_resolution,[],[f992]) ).
fof(f992,plain,
! [X2,X3,X1,X4,X5] :
( ~ rpoint(X3)
| X2 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X2,X2) ),
inference(equality_resolution,[],[f699]) ).
fof(f699,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 != X2
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4
| ~ rpoint(X5)
| X2 != X5
| ~ rR(X1,X0,X2) ),
inference(cnf_transformation,[],[f316]) ).
fof(f1817,plain,
spl52_52,
inference(avatar_split_clause,[],[f1050,f1815]) ).
fof(f1815,plain,
( spl52_52
<=> ! [X1,X3] :
( rreal(sK24(X1,X3))
| ~ rreal(X1)
| ~ rreal(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_52])]) ).
fof(f1050,plain,
! [X3,X1] :
( rreal(sK24(X1,X3))
| ~ rreal(X1)
| ~ rreal(X3) ),
inference(equality_resolution,[],[f1049]) ).
fof(f1049,plain,
! [X2,X3,X1] :
( rreal(sK24(X1,X2))
| ~ rreal(X1)
| ~ rreal(X3)
| X2 != X3 ),
inference(equality_resolution,[],[f720]) ).
fof(f720,plain,
! [X2,X3,X0,X1] :
( rreal(sK24(X0,X2))
| ~ rreal(X1)
| X0 != X1
| ~ rreal(X3)
| X2 != X3 ),
inference(cnf_transformation,[],[f533]) ).
fof(f1813,plain,
spl52_51,
inference(avatar_split_clause,[],[f976,f1811]) ).
fof(f1811,plain,
( spl52_51
<=> ! [X4,X3] :
( rreal(sK19(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_51])]) ).
fof(f976,plain,
! [X3,X4] :
( rreal(sK19(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f975]) ).
fof(f975,plain,
! [X3,X1,X4] :
( rreal(sK19(X3,X1))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4 ),
inference(equality_resolution,[],[f695]) ).
fof(f695,plain,
! [X3,X0,X1,X4] :
( rreal(sK19(X0,X1))
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4 ),
inference(cnf_transformation,[],[f519]) ).
fof(f1809,plain,
spl52_50,
inference(avatar_split_clause,[],[f970,f1807]) ).
fof(f1807,plain,
( spl52_50
<=> ! [X4,X3] :
( rpoint(sK18(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_50])]) ).
fof(f970,plain,
! [X3,X4] :
( rpoint(sK18(X3,X4))
| ~ rpoint(X3)
| ~ rpoint(X4) ),
inference(equality_resolution,[],[f969]) ).
fof(f969,plain,
! [X3,X1,X4] :
( rpoint(sK18(X3,X1))
| ~ rpoint(X3)
| ~ rpoint(X4)
| X1 != X4 ),
inference(equality_resolution,[],[f693]) ).
fof(f693,plain,
! [X3,X0,X1,X4] :
( rpoint(sK18(X0,X1))
| ~ rpoint(X3)
| X0 != X3
| ~ rpoint(X4)
| X1 != X4 ),
inference(cnf_transformation,[],[f516]) ).
fof(f1805,plain,
spl52_49,
inference(avatar_split_clause,[],[f742,f1803]) ).
fof(f1803,plain,
( spl52_49
<=> ! [X0,X1] :
( ron(sK29(X0,X1),X0)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_49])]) ).
fof(f742,plain,
! [X0,X1] :
( ron(sK29(X0,X1),X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
fof(f1801,plain,
spl52_48,
inference(avatar_split_clause,[],[f741,f1799]) ).
fof(f1799,plain,
( spl52_48
<=> ! [X0,X1] :
( ron(sK29(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_48])]) ).
fof(f741,plain,
! [X0,X1] :
( ron(sK29(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
fof(f1797,plain,
( spl52_47
| ~ spl52_1
| ~ spl52_36 ),
inference(avatar_split_clause,[],[f1746,f1734,f1582,f1794]) ).
fof(f1794,plain,
( spl52_47
<=> vd684 = vplus(vd684,vd684) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_47])]) ).
fof(f1582,plain,
( spl52_1
<=> rreal(vd684) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_1])]) ).
fof(f1734,plain,
( spl52_36
<=> ! [X1] :
( vplus(X1,vd684) = X1
| ~ rreal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_36])]) ).
fof(f1746,plain,
( vd684 = vplus(vd684,vd684)
| ~ spl52_1
| ~ spl52_36 ),
inference(resolution,[],[f1735,f1584]) ).
fof(f1584,plain,
( rreal(vd684)
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f1582]) ).
fof(f1735,plain,
( ! [X1] :
( ~ rreal(X1)
| vplus(X1,vd684) = X1 )
| ~ spl52_36 ),
inference(avatar_component_clause,[],[f1734]) ).
fof(f1792,plain,
spl52_46,
inference(avatar_split_clause,[],[f739,f1790]) ).
fof(f1790,plain,
( spl52_46
<=> ! [X0,X1] :
( ron(sK30(X0,X1),X0)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_46])]) ).
fof(f739,plain,
! [X0,X1] :
( ron(sK30(X0,X1),X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
fof(f1788,plain,
spl52_45,
inference(avatar_split_clause,[],[f738,f1786]) ).
fof(f1786,plain,
( spl52_45
<=> ! [X0,X1] :
( ron(sK30(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_45])]) ).
fof(f738,plain,
! [X0,X1] :
( ron(sK30(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
fof(f1784,plain,
spl52_44,
inference(avatar_split_clause,[],[f684,f1782]) ).
fof(f1782,plain,
( spl52_44
<=> ! [X0,X1] :
( ron(sK16(X0,X1),X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_44])]) ).
fof(f684,plain,
! [X0,X1] :
( ron(sK16(X0,X1),X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f1780,plain,
spl52_43,
inference(avatar_split_clause,[],[f683,f1778]) ).
fof(f1778,plain,
( spl52_43
<=> ! [X0,X1] :
( ron(sK16(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_43])]) ).
fof(f683,plain,
! [X0,X1] :
( ron(sK16(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f1776,plain,
spl52_42,
inference(avatar_split_clause,[],[f681,f1774]) ).
fof(f1774,plain,
( spl52_42
<=> ! [X0,X1] :
( ron(sK17(X0,X1),X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_42])]) ).
fof(f681,plain,
! [X0,X1] :
( ron(sK17(X0,X1),X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f1772,plain,
spl52_41,
inference(avatar_split_clause,[],[f680,f1770]) ).
fof(f1770,plain,
( spl52_41
<=> ! [X0,X1] :
( ron(sK17(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_41])]) ).
fof(f680,plain,
! [X0,X1] :
( ron(sK17(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f1768,plain,
spl52_40,
inference(avatar_split_clause,[],[f656,f1766]) ).
fof(f1766,plain,
( spl52_40
<=> ! [X0,X1] :
( sK7(X0,X1) = X0
| ~ rcenter(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_40])]) ).
fof(f656,plain,
! [X0,X1] :
( sK7(X0,X1) = X0
| ~ rcenter(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f490,plain,
! [X0,X1] :
( ( rpoint(sK7(X0,X1))
& sK7(X0,X1) = X0
& rcircle(sK8(X0,X1))
& sK8(X0,X1) = X1 )
| ~ rcenter(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f276,f489]) ).
fof(f489,plain,
! [X0,X1] :
( ? [X2,X3] :
( rpoint(X2)
& X0 = X2
& rcircle(X3)
& X1 = X3 )
=> ( rpoint(sK7(X0,X1))
& sK7(X0,X1) = X0
& rcircle(sK8(X0,X1))
& sK8(X0,X1) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f276,plain,
! [X0,X1] :
( ? [X2,X3] :
( rpoint(X2)
& X0 = X2
& rcircle(X3)
& X1 = X3 )
| ~ rcenter(X0,X1) ),
inference(ennf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( rcenter(X0,X1)
=> ? [X2,X3] :
( rpoint(X2)
& X0 = X2
& rcircle(X3)
& X1 = X3 ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X106,X107] :
( rcenter(X106,X107)
=> ? [X108,X109] :
( rpoint(X108)
& X106 = X108
& rcircle(X109)
& X107 = X109 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(1), 0), imp(cond(axiom(1), 0)))') ).
fof(f1764,plain,
spl52_39,
inference(avatar_split_clause,[],[f654,f1762]) ).
fof(f1762,plain,
( spl52_39
<=> ! [X0,X1] :
( sK8(X0,X1) = X1
| ~ rcenter(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_39])]) ).
fof(f654,plain,
! [X0,X1] :
( sK8(X0,X1) = X1
| ~ rcenter(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f1745,plain,
spl52_38,
inference(avatar_split_clause,[],[f1563,f1742]) ).
fof(f1742,plain,
( spl52_38
<=> rless(vf(vd1128,vd1124),vf(vd1124,vd1126)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_38])]) ).
fof(f1563,plain,
rless(vf(vd1128,vd1124),vf(vd1124,vd1126)),
inference(forward_demodulation,[],[f889,f886]) ).
fof(f886,plain,
vd1130 = vd1124,
inference(definition_unfolding,[],[f620,f884]) ).
fof(f884,plain,
vd1123 = vd1130,
inference(definition_unfolding,[],[f610,f614]) ).
fof(f614,plain,
vd1129 = vd1130,
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
( rpoint(vd1124)
& vd1123 = vd1124
& rpoint(vd1126)
& vd1125 = vd1126
& rpoint(vd1128)
& vd1127 = vd1128
& rpoint(vd1130)
& vd1129 = vd1130
& vd1123 != vd1125
& vd1127 != vd1129
& rless(vf(vd1127,vd1129),vf(vd1123,vd1125)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))') ).
fof(f610,plain,
vd1123 = vd1129,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
vd1123 = vd1129,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(258, 1150, 0)') ).
fof(f620,plain,
vd1123 = vd1124,
inference(cnf_transformation,[],[f13]) ).
fof(f889,plain,
rless(vf(vd1128,vd1130),vf(vd1130,vd1126)),
inference(definition_unfolding,[],[f611,f616,f614,f884,f618]) ).
fof(f618,plain,
vd1125 = vd1126,
inference(cnf_transformation,[],[f13]) ).
fof(f616,plain,
vd1127 = vd1128,
inference(cnf_transformation,[],[f13]) ).
fof(f611,plain,
rless(vf(vd1127,vd1129),vf(vd1123,vd1125)),
inference(cnf_transformation,[],[f13]) ).
fof(f1740,plain,
spl52_37,
inference(avatar_split_clause,[],[f1559,f1738]) ).
fof(f1559,plain,
! [X3] :
( vd684 = vf(X3,X3)
| ~ rpoint(X3) ),
inference(duplicate_literal_removal,[],[f966]) ).
fof(f966,plain,
! [X3] :
( vd684 = vf(X3,X3)
| ~ rpoint(X3)
| ~ rpoint(X3) ),
inference(equality_resolution,[],[f965]) ).
fof(f965,plain,
! [X2,X3] :
( vd684 = vf(X2,X2)
| ~ rpoint(X2)
| ~ rpoint(X3)
| X2 != X3 ),
inference(equality_resolution,[],[f964]) ).
fof(f964,plain,
! [X2,X3,X1] :
( vd684 = vf(X1,X1)
| ~ rpoint(X2)
| X1 != X2
| ~ rpoint(X3)
| X1 != X3 ),
inference(equality_resolution,[],[f920]) ).
fof(f920,plain,
! [X2,X3,X0,X1] :
( vd684 = vf(X0,X1)
| X0 != X1
| ~ rpoint(X2)
| X0 != X2
| ~ rpoint(X3)
| X1 != X3 ),
inference(definition_unfolding,[],[f690,f609]) ).
fof(f690,plain,
! [X2,X3,X0,X1] :
( v0 = vf(X0,X1)
| X0 != X1
| ~ rpoint(X2)
| X0 != X2
| ~ rpoint(X3)
| X1 != X3 ),
inference(cnf_transformation,[],[f513]) ).
fof(f1736,plain,
spl52_36,
inference(avatar_split_clause,[],[f948,f1734]) ).
fof(f948,plain,
! [X1] :
( vplus(X1,vd684) = X1
| ~ rreal(X1) ),
inference(equality_resolution,[],[f918]) ).
fof(f918,plain,
! [X0,X1] :
( vplus(X0,vd684) = X0
| ~ rreal(X1)
| X0 != X1 ),
inference(definition_unfolding,[],[f669,f609]) ).
fof(f669,plain,
! [X0,X1] :
( vplus(X0,v0) = X0
| ~ rreal(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,plain,
! [X0,X1] :
( vplus(X0,v0) = X0
| ~ rreal(X1)
| X0 != X1 ),
inference(flattening,[],[f289]) ).
fof(f289,plain,
! [X0,X1] :
( vplus(X0,v0) = X0
| ~ rreal(X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0,X1] :
( ( rreal(X1)
& X0 = X1 )
=> vplus(X0,v0) = X0 ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X131,X132] :
( ( rreal(X132)
& X131 = X132 )
=> vplus(X131,v0) = X131 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(141), 0), imp(cond(axiom(141), 0)))') ).
fof(f1732,plain,
spl52_35,
inference(avatar_split_clause,[],[f743,f1730]) ).
fof(f1730,plain,
( spl52_35
<=> ! [X0,X1] :
( rpoint(sK29(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_35])]) ).
fof(f743,plain,
! [X0,X1] :
( rpoint(sK29(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
fof(f1728,plain,
spl52_34,
inference(avatar_split_clause,[],[f740,f1726]) ).
fof(f1726,plain,
( spl52_34
<=> ! [X0,X1] :
( rpoint(sK30(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_34])]) ).
fof(f740,plain,
! [X0,X1] :
( rpoint(sK30(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f545]) ).
fof(f1724,plain,
spl52_33,
inference(avatar_split_clause,[],[f685,f1722]) ).
fof(f1722,plain,
( spl52_33
<=> ! [X0,X1] :
( rpoint(sK16(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_33])]) ).
fof(f685,plain,
! [X0,X1] :
( rpoint(sK16(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f1720,plain,
spl52_32,
inference(avatar_split_clause,[],[f682,f1718]) ).
fof(f1718,plain,
( spl52_32
<=> ! [X0,X1] :
( rpoint(sK17(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_32])]) ).
fof(f682,plain,
! [X0,X1] :
( rpoint(sK17(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f512]) ).
fof(f1716,plain,
spl52_31,
inference(avatar_split_clause,[],[f657,f1714]) ).
fof(f1714,plain,
( spl52_31
<=> ! [X0,X1] :
( rpoint(sK7(X0,X1))
| ~ rcenter(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_31])]) ).
fof(f657,plain,
! [X0,X1] :
( rpoint(sK7(X0,X1))
| ~ rcenter(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f1712,plain,
spl52_30,
inference(avatar_split_clause,[],[f655,f1710]) ).
fof(f1710,plain,
( spl52_30
<=> ! [X0,X1] :
( rcircle(sK8(X0,X1))
| ~ rcenter(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_30])]) ).
fof(f655,plain,
! [X0,X1] :
( rcircle(sK8(X0,X1))
| ~ rcenter(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f1708,plain,
spl52_29,
inference(avatar_split_clause,[],[f957,f1706]) ).
fof(f1706,plain,
( spl52_29
<=> ! [X1] :
( sK15(X1) != X1
| ~ rpoint(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_29])]) ).
fof(f957,plain,
! [X1] :
( sK15(X1) != X1
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f677]) ).
fof(f677,plain,
! [X0,X1] :
( sK15(X0) != X0
| ~ rpoint(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f508]) ).
fof(f508,plain,
! [X0,X1] :
( ( rpoint(sK15(X0))
& sK15(X0) != X0 )
| ~ rpoint(X1)
| X0 != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f298,f507]) ).
fof(f507,plain,
! [X0] :
( ? [X2] :
( rpoint(X2)
& X0 != X2 )
=> ( rpoint(sK15(X0))
& sK15(X0) != X0 ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& X0 != X2 )
| ~ rpoint(X1)
| X0 != X1 ),
inference(flattening,[],[f297]) ).
fof(f297,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& X0 != X2 )
| ~ rpoint(X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0,X1] :
( ( rpoint(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& X0 != X2 ) ),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X592,X593] :
( ( rpoint(X593)
& X592 = X593 )
=> ? [X594] :
( rpoint(X594)
& X592 != X594 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(7), 0), imp(cond(axiom(7), 0)))') ).
fof(f1704,plain,
spl52_28,
inference(avatar_split_clause,[],[f955,f1702]) ).
fof(f1702,plain,
( spl52_28
<=> ! [X1] :
( ron(sK14(X1),X1)
| ~ rcircle(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_28])]) ).
fof(f955,plain,
! [X1] :
( ron(sK14(X1),X1)
| ~ rcircle(X1) ),
inference(equality_resolution,[],[f675]) ).
fof(f675,plain,
! [X0,X1] :
( ron(sK14(X0),X0)
| ~ rcircle(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f506]) ).
fof(f506,plain,
! [X0,X1] :
( ( rpoint(sK14(X0))
& ron(sK14(X0),X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f296,f505]) ).
fof(f505,plain,
! [X0] :
( ? [X2] :
( rpoint(X2)
& ron(X2,X0) )
=> ( rpoint(sK14(X0))
& ron(sK14(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f296,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& ron(X2,X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(flattening,[],[f295]) ).
fof(f295,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& ron(X2,X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0,X1] :
( ( rcircle(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& ron(X2,X0) ) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X475,X476] :
( ( rcircle(X476)
& X475 = X476 )
=> ? [X477] :
( rpoint(X477)
& ron(X477,X475) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(41), 0), imp(cond(axiom(41), 0)))') ).
fof(f1700,plain,
spl52_27,
inference(avatar_split_clause,[],[f953,f1698]) ).
fof(f1698,plain,
( spl52_27
<=> ! [X1] :
( rinside(sK13(X1),X1)
| ~ rcircle(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_27])]) ).
fof(f953,plain,
! [X1] :
( rinside(sK13(X1),X1)
| ~ rcircle(X1) ),
inference(equality_resolution,[],[f673]) ).
fof(f673,plain,
! [X0,X1] :
( rinside(sK13(X0),X0)
| ~ rcircle(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f504]) ).
fof(f504,plain,
! [X0,X1] :
( ( rpoint(sK13(X0))
& rinside(sK13(X0),X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f294,f503]) ).
fof(f503,plain,
! [X0] :
( ? [X2] :
( rpoint(X2)
& rinside(X2,X0) )
=> ( rpoint(sK13(X0))
& rinside(sK13(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f294,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& rinside(X2,X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(flattening,[],[f293]) ).
fof(f293,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& rinside(X2,X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1] :
( ( rcircle(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& rinside(X2,X0) ) ),
inference(rectify,[],[f96]) ).
fof(f96,axiom,
! [X460,X461] :
( ( rcircle(X461)
& X460 = X461 )
=> ? [X462] :
( rpoint(X462)
& rinside(X462,X460) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(47), 0), imp(cond(axiom(47), 0)))') ).
fof(f1696,plain,
spl52_26,
inference(avatar_split_clause,[],[f951,f1694]) ).
fof(f1694,plain,
( spl52_26
<=> ! [X1] :
( ~ ron(sK12(X1),X1)
| ~ rcircle(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_26])]) ).
fof(f951,plain,
! [X1] :
( ~ ron(sK12(X1),X1)
| ~ rcircle(X1) ),
inference(equality_resolution,[],[f670]) ).
fof(f670,plain,
! [X0,X1] :
( ~ ron(sK12(X0),X0)
| ~ rcircle(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f502]) ).
fof(f502,plain,
! [X0,X1] :
( ( rpoint(sK12(X0))
& ~ rinside(sK12(X0),X0)
& ~ ron(sK12(X0),X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f292,f501]) ).
fof(f501,plain,
! [X0] :
( ? [X2] :
( rpoint(X2)
& ~ rinside(X2,X0)
& ~ ron(X2,X0) )
=> ( rpoint(sK12(X0))
& ~ rinside(sK12(X0),X0)
& ~ ron(sK12(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f292,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& ~ rinside(X2,X0)
& ~ ron(X2,X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(flattening,[],[f291]) ).
fof(f291,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& ~ rinside(X2,X0)
& ~ ron(X2,X0) )
| ~ rcircle(X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( ( rcircle(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& ~ rinside(X2,X0)
& ~ ron(X2,X0) ) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X196,X197] :
( ( rcircle(X197)
& X196 = X197 )
=> ? [X198] :
( rpoint(X198)
& ~ rinside(X198,X196)
& ~ ron(X198,X196) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(49), 0), imp(cond(axiom(49), 0)))') ).
fof(f1692,plain,
spl52_25,
inference(avatar_split_clause,[],[f950,f1690]) ).
fof(f1690,plain,
( spl52_25
<=> ! [X1] :
( ~ rinside(sK12(X1),X1)
| ~ rcircle(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_25])]) ).
fof(f950,plain,
! [X1] :
( ~ rinside(sK12(X1),X1)
| ~ rcircle(X1) ),
inference(equality_resolution,[],[f671]) ).
fof(f671,plain,
! [X0,X1] :
( ~ rinside(sK12(X0),X0)
| ~ rcircle(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f502]) ).
fof(f1688,plain,
spl52_24,
inference(avatar_split_clause,[],[f946,f1686]) ).
fof(f1686,plain,
( spl52_24
<=> ! [X1] :
( ron(sK11(X1),X1)
| ~ rline(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_24])]) ).
fof(f946,plain,
! [X1] :
( ron(sK11(X1),X1)
| ~ rline(X1) ),
inference(equality_resolution,[],[f666]) ).
fof(f666,plain,
! [X0,X1] :
( ron(sK11(X0),X0)
| ~ rline(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f500]) ).
fof(f500,plain,
! [X0,X1] :
( ( rpoint(sK11(X0))
& ron(sK11(X0),X0) )
| ~ rline(X1)
| X0 != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f286,f499]) ).
fof(f499,plain,
! [X0] :
( ? [X2] :
( rpoint(X2)
& ron(X2,X0) )
=> ( rpoint(sK11(X0))
& ron(sK11(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f286,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& ron(X2,X0) )
| ~ rline(X1)
| X0 != X1 ),
inference(flattening,[],[f285]) ).
fof(f285,plain,
! [X0,X1] :
( ? [X2] :
( rpoint(X2)
& ron(X2,X0) )
| ~ rline(X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( ( rline(X1)
& X0 = X1 )
=> ? [X2] :
( rpoint(X2)
& ron(X2,X0) ) ),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X568,X569] :
( ( rline(X569)
& X568 = X569 )
=> ? [X570] :
( rpoint(X570)
& ron(X570,X568) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(15), 0), imp(cond(axiom(15), 0)))') ).
fof(f1684,plain,
spl52_23,
inference(avatar_split_clause,[],[f653,f1682]) ).
fof(f1682,plain,
( spl52_23
<=> ! [X0,X1] :
( rinside(X0,X1)
| ~ rcenter(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_23])]) ).
fof(f653,plain,
! [X0,X1] :
( rinside(X0,X1)
| ~ rcenter(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0,X1] :
( rinside(X0,X1)
| ~ rcenter(X0,X1) ),
inference(ennf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( rcenter(X0,X1)
=> rinside(X0,X1) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X139,X140] :
( rcenter(X139,X140)
=> rinside(X139,X140) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))') ).
fof(f1680,plain,
spl52_22,
inference(avatar_split_clause,[],[f956,f1678]) ).
fof(f1678,plain,
( spl52_22
<=> ! [X1] :
( rpoint(sK15(X1))
| ~ rpoint(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_22])]) ).
fof(f956,plain,
! [X1] :
( rpoint(sK15(X1))
| ~ rpoint(X1) ),
inference(equality_resolution,[],[f678]) ).
fof(f678,plain,
! [X0,X1] :
( rpoint(sK15(X0))
| ~ rpoint(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f508]) ).
fof(f1676,plain,
spl52_21,
inference(avatar_split_clause,[],[f954,f1674]) ).
fof(f1674,plain,
( spl52_21
<=> ! [X1] :
( rpoint(sK14(X1))
| ~ rcircle(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_21])]) ).
fof(f954,plain,
! [X1] :
( rpoint(sK14(X1))
| ~ rcircle(X1) ),
inference(equality_resolution,[],[f676]) ).
fof(f676,plain,
! [X0,X1] :
( rpoint(sK14(X0))
| ~ rcircle(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f506]) ).
fof(f1672,plain,
spl52_20,
inference(avatar_split_clause,[],[f952,f1670]) ).
fof(f1670,plain,
( spl52_20
<=> ! [X1] :
( rpoint(sK13(X1))
| ~ rcircle(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_20])]) ).
fof(f952,plain,
! [X1] :
( rpoint(sK13(X1))
| ~ rcircle(X1) ),
inference(equality_resolution,[],[f674]) ).
fof(f674,plain,
! [X0,X1] :
( rpoint(sK13(X0))
| ~ rcircle(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f504]) ).
fof(f1668,plain,
spl52_19,
inference(avatar_split_clause,[],[f949,f1666]) ).
fof(f1666,plain,
( spl52_19
<=> ! [X1] :
( rpoint(sK12(X1))
| ~ rcircle(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_19])]) ).
fof(f949,plain,
! [X1] :
( rpoint(sK12(X1))
| ~ rcircle(X1) ),
inference(equality_resolution,[],[f672]) ).
fof(f672,plain,
! [X0,X1] :
( rpoint(sK12(X0))
| ~ rcircle(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f502]) ).
fof(f1664,plain,
spl52_18,
inference(avatar_split_clause,[],[f947,f1662]) ).
fof(f1662,plain,
( spl52_18
<=> ! [X1] :
( ~ rless(X1,X1)
| ~ rreal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_18])]) ).
fof(f947,plain,
! [X1] :
( ~ rless(X1,X1)
| ~ rreal(X1) ),
inference(equality_resolution,[],[f668]) ).
fof(f668,plain,
! [X0,X1] :
( ~ rless(X0,X0)
| ~ rreal(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0,X1] :
( ~ rless(X0,X0)
| ~ rreal(X1)
| X0 != X1 ),
inference(flattening,[],[f287]) ).
fof(f287,plain,
! [X0,X1] :
( ~ rless(X0,X0)
| ~ rreal(X1)
| X0 != X1 ),
inference(ennf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0,X1] :
( ( rreal(X1)
& X0 = X1 )
=> ~ rless(X0,X0) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X62,X63] :
( ( rreal(X63)
& X62 = X63 )
=> ~ rless(X62,X62) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(149), 0), imp(cond(axiom(149), 0)))') ).
fof(f1660,plain,
spl52_17,
inference(avatar_split_clause,[],[f945,f1658]) ).
fof(f1658,plain,
( spl52_17
<=> ! [X1] :
( rpoint(sK11(X1))
| ~ rline(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_17])]) ).
fof(f945,plain,
! [X1] :
( rpoint(sK11(X1))
| ~ rline(X1) ),
inference(equality_resolution,[],[f667]) ).
fof(f667,plain,
! [X0,X1] :
( rpoint(sK11(X0))
| ~ rline(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f500]) ).
fof(f1655,plain,
( spl52_16
| ~ spl52_10
| ~ spl52_14 ),
inference(avatar_split_clause,[],[f1651,f1643,f1625,f1653]) ).
fof(f1625,plain,
( spl52_10
<=> vd1130 = vd1124 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_10])]) ).
fof(f1643,plain,
( spl52_14
<=> ! [X0] :
( ~ rline(X0)
| ~ ron(vd1126,X0)
| ~ ron(vd1130,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_14])]) ).
fof(f1651,plain,
( ! [X0] :
( ~ ron(vd1124,X0)
| ~ rline(X0)
| ~ ron(vd1126,X0) )
| ~ spl52_10
| ~ spl52_14 ),
inference(forward_demodulation,[],[f1644,f1627]) ).
fof(f1627,plain,
( vd1130 = vd1124
| ~ spl52_10 ),
inference(avatar_component_clause,[],[f1625]) ).
fof(f1644,plain,
( ! [X0] :
( ~ rline(X0)
| ~ ron(vd1126,X0)
| ~ ron(vd1130,X0) )
| ~ spl52_14 ),
inference(avatar_component_clause,[],[f1643]) ).
fof(f1650,plain,
( spl52_15
| ~ spl52_10
| ~ spl52_13 ),
inference(avatar_split_clause,[],[f1646,f1640,f1625,f1648]) ).
fof(f1640,plain,
( spl52_13
<=> ! [X1] :
( ~ rcircle(X1)
| ~ ron(vd1128,X1)
| ~ rcenter(vd1130,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_13])]) ).
fof(f1646,plain,
( ! [X1] :
( ~ rcenter(vd1124,X1)
| ~ rcircle(X1)
| ~ ron(vd1128,X1) )
| ~ spl52_10
| ~ spl52_13 ),
inference(forward_demodulation,[],[f1641,f1627]) ).
fof(f1641,plain,
( ! [X1] :
( ~ rcircle(X1)
| ~ ron(vd1128,X1)
| ~ rcenter(vd1130,X1) )
| ~ spl52_13 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f1645,plain,
( spl52_13
| spl52_14 ),
inference(avatar_split_clause,[],[f885,f1643,f1640]) ).
fof(f885,plain,
! [X0,X1] :
( ~ rline(X0)
| ~ ron(vd1130,X0)
| ~ ron(vd1126,X0)
| ~ rcircle(X1)
| ~ rcenter(vd1130,X1)
| ~ ron(vd1128,X1) ),
inference(definition_unfolding,[],[f606,f884,f618,f884,f616]) ).
fof(f606,plain,
! [X0,X1] :
( ~ rline(X0)
| ~ ron(vd1123,X0)
| ~ ron(vd1125,X0)
| ~ rcircle(X1)
| ~ rcenter(vd1123,X1)
| ~ ron(vd1127,X1) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0,X1] :
( ~ rline(X0)
| ~ ron(vd1123,X0)
| ~ ron(vd1125,X0)
| ~ rcircle(X1)
| ~ rcenter(vd1123,X1)
| ~ ron(vd1127,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ? [X0,X1] :
( rline(X0)
& ron(vd1123,X0)
& ron(vd1125,X0)
& rcircle(X1)
& rcenter(vd1123,X1)
& ron(vd1127,X1) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
? [X0,X1] :
( rline(X0)
& ron(vd1123,X0)
& ron(vd1125,X0)
& rcircle(X1)
& rcenter(vd1123,X1)
& ron(vd1127,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(259)') ).
fof(f1638,plain,
~ spl52_12,
inference(avatar_split_clause,[],[f1562,f1635]) ).
fof(f1562,plain,
vd1128 != vd1124,
inference(forward_demodulation,[],[f888,f886]) ).
fof(f888,plain,
vd1130 != vd1128,
inference(definition_unfolding,[],[f612,f616,f614]) ).
fof(f612,plain,
vd1127 != vd1129,
inference(cnf_transformation,[],[f13]) ).
fof(f1633,plain,
~ spl52_11,
inference(avatar_split_clause,[],[f1561,f1630]) ).
fof(f1561,plain,
vd1126 != vd1124,
inference(forward_demodulation,[],[f887,f886]) ).
fof(f887,plain,
vd1130 != vd1126,
inference(definition_unfolding,[],[f613,f884,f618]) ).
fof(f613,plain,
vd1123 != vd1125,
inference(cnf_transformation,[],[f13]) ).
fof(f1628,plain,
spl52_10,
inference(avatar_split_clause,[],[f886,f1625]) ).
fof(f1623,plain,
( ~ spl52_8
| spl52_9 ),
inference(avatar_split_clause,[],[f649,f1620,f1616]) ).
fof(f1616,plain,
( spl52_8
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_8])]) ).
fof(f1620,plain,
( spl52_9
<=> rcircle(vskolem1139) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_9])]) ).
fof(f649,plain,
( rcircle(vskolem1139)
| ~ sP1 ),
inference(cnf_transformation,[],[f488]) ).
fof(f488,plain,
( ( ron(vd1123,vskolem1138)
& ron(vd1125,vskolem1138)
& rcircle(vskolem1139)
& rcenter(vd1123,vskolem1139)
& ron(vskolem1136,vskolem1139) )
| ~ sP1 ),
inference(nnf_transformation,[],[f475]) ).
fof(f475,plain,
( ( ron(vd1123,vskolem1138)
& ron(vd1125,vskolem1138)
& rcircle(vskolem1139)
& rcenter(vd1123,vskolem1139)
& ron(vskolem1136,vskolem1139) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f1614,plain,
( ~ spl52_6
| spl52_7 ),
inference(avatar_split_clause,[],[f632,f1611,f1607]) ).
fof(f1607,plain,
( spl52_6
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl52_6])]) ).
fof(f1611,plain,
( spl52_7
<=> rcircle(vskolem1146) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_7])]) ).
fof(f632,plain,
( rcircle(vskolem1146)
| ~ sP0 ),
inference(cnf_transformation,[],[f487]) ).
fof(f487,plain,
( ( ron(vd1123,vskolem1145)
& ron(vd1125,vskolem1145)
& rcircle(vskolem1146)
& rcenter(vd1123,vskolem1146)
& ron(vd1129,vskolem1146) )
| ~ sP0 ),
inference(nnf_transformation,[],[f473]) ).
fof(f473,plain,
( ( ron(vd1123,vskolem1145)
& ron(vd1125,vskolem1145)
& rcircle(vskolem1146)
& rcenter(vd1123,vskolem1146)
& ron(vd1129,vskolem1146) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f1605,plain,
spl52_5,
inference(avatar_split_clause,[],[f621,f1602]) ).
fof(f621,plain,
rpoint(vd1124),
inference(cnf_transformation,[],[f13]) ).
fof(f1600,plain,
spl52_4,
inference(avatar_split_clause,[],[f619,f1597]) ).
fof(f619,plain,
rpoint(vd1126),
inference(cnf_transformation,[],[f13]) ).
fof(f1595,plain,
spl52_3,
inference(avatar_split_clause,[],[f617,f1592]) ).
fof(f617,plain,
rpoint(vd1128),
inference(cnf_transformation,[],[f13]) ).
fof(f1590,plain,
spl52_2,
inference(avatar_split_clause,[],[f608,f1587]) ).
fof(f608,plain,
rpoint(vd14),
inference(cnf_transformation,[],[f117]) ).
fof(f117,axiom,
rpoint(vd14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(5), 0)') ).
fof(f1585,plain,
spl52_1,
inference(avatar_split_clause,[],[f607,f1582]) ).
fof(f607,plain,
rreal(vd684),
inference(cnf_transformation,[],[f68]) ).
fof(f68,axiom,
rreal(vd684),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','pred(axiom(137), 1)') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO284+1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n018.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 3 22:03:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (1638)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (1643)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (1641)WARNING: value z3 for option sas not known
% 0.15/0.38 % (1640)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (1642)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (1641)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (1644)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (1639)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (1645)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.42 % (1643)First to succeed.
% 0.22/0.44 % (1643)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1638"
% 0.22/0.44 % (1643)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (1643)------------------------------
% 0.22/0.45 % (1643)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.45 % (1643)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (1643)Memory used [KB]: 2750
% 0.22/0.45 % (1643)Time elapsed: 0.057 s
% 0.22/0.45 % (1643)Instructions burned: 142 (million)
% 0.22/0.45 % (1638)Success in time 0.084 s
%------------------------------------------------------------------------------