TSTP Solution File: GRP212-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRP212-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 11:52:34 EDT 2024
% Result : Unsatisfiable 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 45
% Syntax : Number of formulae : 839 ( 169 unt; 0 def)
% Number of atoms : 2305 (1050 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 2755 (1289 ~;1455 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 567 ( 567 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3609,plain,
$false,
inference(avatar_sat_refutation,[],[f45,f286,f324,f1962,f2127,f2131,f2403,f2509,f2513,f2518,f2521,f2525,f2528,f2531,f2534,f2538,f2541,f2543,f2545,f2549,f2552,f2555,f2557,f2754,f2799,f2803,f2805,f2837,f2842,f2844,f2846,f2848,f2857,f2865,f2891,f2893,f2895,f2897,f2900,f2904,f2907,f2909,f2912,f3146,f3412,f3587,f3591,f3596,f3608]) ).
fof(f3608,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_8
| spl0_9
| spl0_10 ),
inference(avatar_contradiction_clause,[],[f3607]) ).
fof(f3607,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_8
| spl0_9
| spl0_10 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f46,f3,f63,f60,f193,f36,f32,f31,f33,f28,f26,f25,f16,f4,f27,f22,f40,f293,f296,f200,f299,f294,f292,f303,f297,f308,f300,f309,f311,f189,f313,f23,f196,f363,f364,f366,f367,f360,f372,f373,f361,f369,f362,f302,f388,f389,f384,f398,f395,f306,f513,f515,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1902,f1963,f1889,f1779,f1776,f1775,f1840,f1968,f1970,f1974,f1757,f1754,f1640,f1639,f1638,f1636,f1635,f1626,f1625,f1620,f1978,f1980,f1605,f1981,f1602,f1598,f1561,f1555,f1538,f1430,f1421,f1409,f1408,f1403,f1402,f1986,f1987,f1397,f1396,f1245,f1244,f1243,f1241,f1240,f1233,f1232,f2000,f2001,f1223,f1221,f2002,f2009,f2010,f1155,f1154,f1141,f1001,f1000,f996,f2023,f994,f993,f2024,f991,f990,f1097,f2032,f962,f2036,f811,f2039,f751,f2042,f20,f2051,f2052,f626,f624,f2059,f21,f2063,f2093,f2094,f2095,f2096,f1140,f2062,f9,f7,f8,f14,f13,f15,f2122,f2132,f2133,f2146,f2147,f2137,f2138,f2148,f2140,f2141,f2142,f2143,f2145,f1406,f1996,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f1843,f1158,f1226,f1997,f1398,f1621,f1903,f2424,f1758,f1637,f1627,f1242,f1234,f1002,f1144,f5,f2006,f2044,f1442,f2019,f1583,f2034,f1873,f2041,f44,f3077,f3078,f3087,f3082,f3085,f3086,f736,f3101,f3102,f3106,f3107,f3075,f3137,f3076,f3176,f3177,f3181,f3182,f3084,f3202,f3203,f3208,f3212,f3213,f3214,f3215,f3105,f3232,f3233,f3238,f3242,f3243,f3244,f3245,f3083,f3300,f3264,f3301,f3272,f3287,f3288,f3291,f3292,f3104,f3376,f3338,f3377,f3347,f3355,f3363,f3364,f3367,f3368,f3358,f3398,f3354,f3349,f3345,f3326,f3282,f3279,f3276,f3270,f3251,f3216,f3209,f3221,f3218,f3199,f3097,f3081,f3109,f3096,f737,f752,f2149,f2426,f2427,f812,f2003,f1445,f1879,f1586,f24,f3418,f30,f3419,f29,f17,f6,f3422,f18,f3425,f1424,f386,f392,f898,f948,f953,f2433,f3428,f3429,f3430,f3431,f1431,f2724,f1599,f1890,f3432,f1412,f3433,f1606,f2038,f3434,f1539,f2356,f2125,f3080,f3511,f2311,f3519,f3520,f3521,f3522,f3527,f3528,f3598,f3436,f3599,f19,f3600,f3602,f3140]) ).
fof(f3140,plain,
( identity != sk_c6
| spl0_10 ),
inference(avatar_component_clause,[],[f3139]) ).
fof(f3139,plain,
( spl0_10
<=> identity = sk_c6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f3602,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_2
| spl0_9 ),
inference(subsumption_resolution,[],[f3601,f2125]) ).
fof(f3601,plain,
( identity = sk_c8
| sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f7,f3080]) ).
fof(f3600,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_2
| spl0_9 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f46,f3,f63,f60,f193,f36,f32,f31,f33,f28,f26,f25,f16,f4,f27,f22,f200,f299,f297,f308,f189,f313,f23,f196,f363,f364,f366,f367,f360,f372,f373,f361,f369,f362,f306,f513,f515,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1902,f1963,f1889,f1776,f1775,f1840,f1968,f1970,f1974,f1757,f1754,f1639,f1638,f1636,f1635,f1626,f1625,f1620,f1978,f1980,f1605,f1981,f1602,f1598,f1561,f1555,f1538,f1430,f1421,f1409,f1408,f1403,f1402,f1986,f1987,f1397,f1396,f1244,f1243,f1241,f1240,f1233,f1232,f2000,f2001,f1223,f1221,f2002,f2009,f2010,f1155,f1154,f1141,f1001,f1000,f993,f2024,f991,f990,f1097,f2032,f962,f811,f2039,f751,f2042,f20,f2051,f2052,f626,f624,f2059,f21,f2063,f2093,f2094,f2095,f2096,f1140,f2062,f9,f7,f8,f14,f13,f15,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f5,f2006,f2044,f1442,f2019,f1583,f2034,f1873,f2041,f44,f3077,f3078,f3087,f3082,f3085,f3086,f736,f3101,f3102,f3106,f3107,f3075,f3137,f3076,f3176,f3177,f3181,f3182,f3084,f3202,f3203,f3208,f3212,f3213,f3214,f3215,f3105,f3232,f3233,f3238,f3242,f3243,f3244,f3245,f3083,f3300,f3264,f3301,f3272,f3287,f3288,f3291,f3292,f3104,f3376,f3338,f3377,f3347,f3355,f3363,f3364,f3367,f3368,f3398,f3349,f3326,f3276,f3216,f3209,f3199,f3097,f3081,f3109,f3096,f24,f3418,f30,f3419,f29,f17,f6,f3422,f18,f3425,f2125,f3080,f3511,f19]) ).
fof(f19,axiom,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = multiply(sk_c2,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f3599,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_2
| ~ spl0_8
| spl0_9 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f46,f3,f63,f60,f193,f36,f32,f31,f33,f28,f26,f25,f16,f4,f27,f22,f40,f293,f296,f200,f299,f294,f292,f303,f297,f308,f300,f309,f311,f189,f313,f23,f196,f363,f364,f366,f367,f360,f372,f373,f361,f369,f362,f302,f388,f389,f384,f398,f395,f306,f513,f515,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1902,f1963,f1889,f1779,f1776,f1775,f1840,f1968,f1970,f1974,f1757,f1754,f1640,f1639,f1638,f1636,f1635,f1626,f1625,f1620,f1978,f1980,f1605,f1981,f1602,f1598,f1561,f1555,f1538,f1430,f1421,f1409,f1408,f1403,f1402,f1986,f1987,f1397,f1396,f1245,f1244,f1243,f1241,f1240,f1233,f1232,f2000,f2001,f1223,f1221,f2002,f2009,f2010,f1155,f1154,f1141,f1001,f1000,f996,f2023,f994,f993,f2024,f991,f990,f1097,f2032,f962,f2036,f811,f2039,f751,f2042,f20,f19,f2051,f2052,f626,f624,f2059,f21,f2063,f2093,f2094,f2095,f2096,f1140,f2062,f9,f7,f8,f14,f13,f15,f2122,f2132,f2133,f2146,f2147,f2137,f2138,f2148,f2140,f2141,f2142,f2143,f2145,f1406,f1996,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f1843,f1158,f1226,f1997,f1398,f1621,f1903,f2424,f1758,f1637,f1627,f1242,f1234,f1002,f1144,f5,f2006,f2044,f1442,f2019,f1583,f2034,f1873,f2041,f44,f3077,f3078,f3087,f3082,f3085,f3086,f736,f3101,f3102,f3106,f3107,f3075,f3137,f3076,f3176,f3177,f3181,f3182,f3084,f3202,f3203,f3208,f3212,f3213,f3214,f3215,f3105,f3232,f3233,f3238,f3242,f3243,f3244,f3245,f3083,f3300,f3264,f3301,f3272,f3287,f3288,f3291,f3292,f3104,f3376,f3338,f3377,f3347,f3355,f3363,f3364,f3367,f3368,f3358,f3398,f3354,f3349,f3345,f3326,f3282,f3279,f3276,f3270,f3251,f3216,f3209,f3221,f3218,f3199,f3097,f3081,f3109,f3096,f737,f752,f2149,f2426,f2427,f812,f2003,f1445,f1879,f1586,f24,f3418,f30,f3419,f29,f17,f6,f3422,f18,f3425,f1424,f386,f392,f898,f948,f953,f2433,f3428,f3429,f3430,f3431,f1431,f2724,f1599,f1890,f3432,f1412,f3433,f1606,f2038,f3434,f1539,f2356,f2125,f3080,f3511,f2311,f3519,f3520,f3521,f3522,f3527,f3528,f3598,f3436]) ).
fof(f3436,plain,
( identity = sk_c6
| sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f3435,f293]) ).
fof(f3435,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f20,f2145]) ).
fof(f3598,plain,
( identity = sk_c6
| ~ spl0_1
| ~ spl0_2
| ~ spl0_8
| spl0_9 ),
inference(subsumption_resolution,[],[f3597,f2125]) ).
fof(f3597,plain,
( identity = sk_c8
| identity = sk_c6
| ~ spl0_1
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f3438,f3080]) ).
fof(f3438,plain,
( identity = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f3437,f293]) ).
fof(f3437,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| multiply(sk_c1,sk_c2) = sk_c8
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f8,f2145]) ).
fof(f3528,plain,
( ! [X0] : sk_c8 = multiply(X0,inverse(multiply(sk_c7,X0)))
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f1308,f2311]) ).
fof(f3527,plain,
( ! [X0] : inverse(multiply(sk_c7,X0)) = multiply(inverse(X0),sk_c8)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f1314,f2311]) ).
fof(f3522,plain,
( multiply(sk_c8,sk_c1) = inverse(multiply(sk_c2,sk_c7))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f2311,f3083]) ).
fof(f3521,plain,
( multiply(sk_c8,sk_c2) = inverse(multiply(sk_c1,sk_c7))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f2311,f3104]) ).
fof(f3520,plain,
( ! [X0] : multiply(sk_c8,X0) = inverse(multiply(inverse(X0),sk_c7))
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f2311,f1190]) ).
fof(f3519,plain,
( ! [X0] : inverse(multiply(X0,sk_c7)) = multiply(sk_c8,inverse(X0))
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f2311,f1186]) ).
fof(f2311,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2133,f2145]) ).
fof(f3511,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3502,f1]) ).
fof(f3502,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c1,multiply(sk_c2,X0))
| ~ spl0_2 ),
inference(superposition,[],[f3,f3080]) ).
fof(f3080,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f715,f44]) ).
fof(f2125,plain,
( identity != sk_c8
| spl0_9 ),
inference(avatar_component_clause,[],[f2124]) ).
fof(f2124,plain,
( spl0_9
<=> identity = sk_c8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f2356,plain,
( ! [X0] : multiply(multiply(X0,sk_c7),sk_c8) = X0
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2141,f2145]) ).
fof(f1539,plain,
( ! [X0] : multiply(multiply(X0,sk_c7),sk_c8) = X0
| ~ spl0_1 ),
inference(superposition,[],[f1429,f40]) ).
fof(f3434,plain,
( identity != sk_c8
| ~ spl0_1
| spl0_9 ),
inference(global_subsumption,[],[f2038,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f33,f28,f26,f25,f16,f4,f27,f22,f189,f313,f23,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f21,f9,f7,f8,f14,f13,f15,f2125,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f5,f24,f30,f29,f17,f6,f18]) ).
fof(f2038,plain,
( ! [X3,X8,X6,X5] :
( sk_c7 != multiply(identity,X8)
| identity != sk_c8
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(X6,sk_c7)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2037,f718]) ).
fof(f2037,plain,
( ! [X3,X8,X6,X5] :
( identity != sk_c8
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| sk_c7 != multiply(identity,multiply(X8,identity))
| identity != multiply(X6,sk_c7)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1 ),
inference(inner_rewriting,[],[f2036]) ).
fof(f1606,plain,
( ! [X0] : sk_c7 = multiply(X0,inverse(multiply(sk_c8,X0)))
| ~ spl0_1 ),
inference(superposition,[],[f1190,f302]) ).
fof(f3433,plain,
( ! [X0] : sk_c7 = multiply(X0,inverse(multiply(sk_c8,X0)))
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2140,f2145]) ).
fof(f1412,plain,
( ! [X0] : sk_c7 = multiply(X0,inverse(multiply(sk_c8,X0)))
| ~ spl0_1 ),
inference(superposition,[],[f1308,f292]) ).
fof(f3432,plain,
( ! [X0] : sk_c7 = multiply(inverse(multiply(X0,sk_c8)),X0)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2143,f2145]) ).
fof(f1890,plain,
( ! [X0] : sk_c8 = multiply(inverse(multiply(X0,sk_c7)),X0)
| ~ spl0_1 ),
inference(superposition,[],[f1691,f40]) ).
fof(f1599,plain,
( ! [X0] : sk_c8 = multiply(X0,inverse(multiply(sk_c7,X0)))
| ~ spl0_1 ),
inference(superposition,[],[f1190,f40]) ).
fof(f2724,plain,
( ! [X0] : multiply(multiply(X0,sk_c8),sk_c7) = X0
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2142,f2145]) ).
fof(f1431,plain,
( ! [X0] : multiply(multiply(X0,sk_c8),sk_c7) = X0
| ~ spl0_1 ),
inference(superposition,[],[f1308,f40]) ).
fof(f3431,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2705,f718]) ).
fof(f2705,plain,
( multiply(sk_c8,identity) = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1398,f1144]) ).
fof(f3430,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2695,f718]) ).
fof(f2695,plain,
( multiply(sk_c8,identity) = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1997,f1144]) ).
fof(f3429,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2692,f718]) ).
fof(f2692,plain,
( multiply(sk_c8,identity) = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1621,f1144]) ).
fof(f3428,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2689,f718]) ).
fof(f2689,plain,
( multiply(sk_c8,identity) = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1226,f1144]) ).
fof(f2433,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_1 ),
inference(forward_demodulation,[],[f397,f1]) ).
fof(f397,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c7,X0))
| ~ spl0_1 ),
inference(superposition,[],[f3,f384]) ).
fof(f953,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_1 ),
inference(forward_demodulation,[],[f928,f199]) ).
fof(f928,plain,
( ! [X0] : multiply(sk_c8,multiply(inverse(inverse(sk_c7)),X0)) = X0
| ~ spl0_1 ),
inference(superposition,[],[f302,f719]) ).
fof(f948,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_1 ),
inference(forward_demodulation,[],[f921,f199]) ).
fof(f921,plain,
( ! [X0] : multiply(sk_c8,multiply(inverse(inverse(sk_c7)),X0)) = X0
| ~ spl0_1 ),
inference(superposition,[],[f719,f302]) ).
fof(f898,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_1 ),
inference(superposition,[],[f719,f40]) ).
fof(f392,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_1 ),
inference(superposition,[],[f60,f302]) ).
fof(f386,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_1 ),
inference(superposition,[],[f302,f60]) ).
fof(f1424,plain,
( sk_c8 = multiply(identity,inverse(sk_c7))
| ~ spl0_1 ),
inference(superposition,[],[f1308,f384]) ).
fof(f3425,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_2
| spl0_9 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f46,f3,f63,f60,f193,f36,f32,f31,f33,f28,f26,f25,f16,f4,f27,f22,f200,f299,f297,f308,f189,f313,f23,f196,f363,f364,f366,f367,f360,f372,f373,f361,f369,f362,f306,f513,f515,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1902,f1963,f1889,f1776,f1775,f1840,f1968,f1970,f1974,f1757,f1754,f1639,f1638,f1636,f1635,f1626,f1625,f1620,f1978,f1980,f1605,f1981,f1602,f1598,f1561,f1555,f1538,f1430,f1421,f1409,f1408,f1403,f1402,f1986,f1987,f1397,f1396,f1244,f1243,f1241,f1240,f1233,f1232,f2000,f2001,f1223,f1221,f2002,f2009,f2010,f1155,f1154,f1141,f1001,f1000,f993,f2024,f991,f990,f1097,f2032,f962,f811,f2039,f751,f2042,f20,f19,f2051,f2052,f626,f624,f2059,f21,f2063,f2093,f2094,f2095,f2096,f1140,f2062,f9,f7,f8,f14,f13,f15,f2125,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f5,f2006,f2044,f1442,f2019,f1583,f2034,f1873,f2041,f44,f3077,f3078,f3087,f3082,f3085,f3086,f736,f3101,f3102,f3106,f3107,f3075,f3137,f3076,f3176,f3177,f3181,f3182,f3084,f3202,f3203,f3208,f3212,f3213,f3214,f3215,f3105,f3232,f3233,f3238,f3242,f3243,f3244,f3245,f3083,f3300,f3264,f3301,f3272,f3287,f3288,f3291,f3292,f3104,f3376,f3338,f3377,f3347,f3355,f3363,f3364,f3367,f3368,f3398,f3349,f3326,f3276,f3216,f3209,f3199,f3097,f3081,f3109,f3096,f3080,f24,f3418,f30,f3419,f29,f17,f6,f3422,f18]) ).
fof(f18,axiom,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f3422,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_2
| spl0_9 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f46,f3,f63,f60,f193,f36,f32,f31,f33,f28,f26,f25,f16,f4,f27,f22,f200,f299,f297,f308,f189,f313,f23,f196,f363,f364,f366,f367,f360,f372,f373,f361,f369,f362,f306,f513,f515,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1902,f1963,f1889,f1776,f1775,f1840,f1968,f1970,f1974,f1757,f1754,f1639,f1638,f1636,f1635,f1626,f1625,f1620,f1978,f1980,f1605,f1981,f1602,f1598,f1561,f1555,f1538,f1430,f1421,f1409,f1408,f1403,f1402,f1986,f1987,f1397,f1396,f1244,f1243,f1241,f1240,f1233,f1232,f2000,f2001,f1223,f1221,f2002,f2009,f2010,f1155,f1154,f1141,f1001,f1000,f993,f2024,f991,f990,f1097,f2032,f962,f811,f2039,f751,f2042,f20,f19,f18,f2051,f2052,f626,f624,f2059,f21,f2063,f2093,f2094,f2095,f2096,f1140,f2062,f9,f7,f8,f14,f13,f15,f2125,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f5,f2006,f2044,f1442,f2019,f1583,f2034,f1873,f2041,f44,f3077,f3078,f3087,f3082,f3085,f3086,f736,f3101,f3102,f3106,f3107,f3075,f3137,f3076,f3176,f3177,f3181,f3182,f3084,f3202,f3203,f3208,f3212,f3213,f3214,f3215,f3105,f3232,f3233,f3238,f3242,f3243,f3244,f3245,f3083,f3300,f3264,f3301,f3272,f3287,f3288,f3291,f3292,f3104,f3376,f3338,f3377,f3347,f3355,f3363,f3364,f3367,f3368,f3398,f3349,f3326,f3276,f3216,f3209,f3199,f3097,f3081,f3109,f3096,f3080,f24,f3418,f30,f3419,f29,f17,f6]) ).
fof(f6,axiom,
( sk_c8 = multiply(sk_c4,sk_c7)
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f17,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c2,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f29,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f3419,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_2
| spl0_9 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f46,f3,f63,f60,f193,f36,f32,f31,f6,f33,f29,f28,f26,f25,f16,f4,f27,f22,f200,f299,f297,f308,f189,f313,f23,f196,f363,f364,f366,f367,f360,f372,f373,f361,f369,f362,f306,f513,f515,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1902,f1963,f1889,f1776,f1775,f1840,f1968,f1970,f1974,f1757,f1754,f1639,f1638,f1636,f1635,f1626,f1625,f1620,f1978,f1980,f1605,f1981,f1602,f1598,f1561,f1555,f1538,f1430,f1421,f1409,f1408,f1403,f1402,f1986,f1987,f1397,f1396,f1244,f1243,f1241,f1240,f1233,f1232,f2000,f2001,f1223,f1221,f2002,f2009,f2010,f1155,f1154,f1141,f1001,f1000,f993,f2024,f991,f990,f1097,f2032,f962,f811,f2039,f751,f2042,f20,f19,f18,f2051,f2052,f626,f624,f2059,f21,f17,f2063,f2093,f2094,f2095,f2096,f1140,f2062,f9,f7,f8,f14,f13,f15,f2125,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f5,f2006,f2044,f1442,f2019,f1583,f2034,f1873,f2041,f44,f3077,f3078,f3087,f3082,f3085,f3086,f736,f3101,f3102,f3106,f3107,f3075,f3137,f3076,f3176,f3177,f3181,f3182,f3084,f3202,f3203,f3208,f3212,f3213,f3214,f3215,f3105,f3232,f3233,f3238,f3242,f3243,f3244,f3245,f3083,f3300,f3264,f3301,f3272,f3287,f3288,f3291,f3292,f3104,f3376,f3338,f3377,f3347,f3355,f3363,f3364,f3367,f3368,f3398,f3349,f3326,f3276,f3216,f3209,f3199,f3097,f3081,f3109,f3096,f3080,f24,f3418,f30]) ).
fof(f30,axiom,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f3418,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_2
| spl0_9 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f46,f3,f63,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f16,f4,f27,f22,f200,f299,f297,f308,f189,f313,f23,f196,f363,f364,f366,f367,f360,f372,f373,f361,f369,f362,f306,f513,f515,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1902,f1963,f1889,f1776,f1775,f1840,f1968,f1970,f1974,f1757,f1754,f1639,f1638,f1636,f1635,f1626,f1625,f1620,f1978,f1980,f1605,f1981,f1602,f1598,f1561,f1555,f1538,f1430,f1421,f1409,f1408,f1403,f1402,f1986,f1987,f1397,f1396,f1244,f1243,f1241,f1240,f1233,f1232,f2000,f2001,f1223,f1221,f2002,f2009,f2010,f1155,f1154,f1141,f1001,f1000,f993,f2024,f991,f990,f1097,f2032,f962,f811,f2039,f751,f2042,f20,f19,f18,f2051,f2052,f626,f624,f2059,f21,f17,f2063,f2093,f2094,f2095,f2096,f1140,f2062,f9,f7,f8,f14,f13,f15,f2125,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f5,f2006,f2044,f1442,f2019,f1583,f2034,f1873,f2041,f44,f3077,f3078,f3087,f3082,f3085,f3086,f736,f3101,f3102,f3106,f3107,f3075,f3137,f3076,f3176,f3177,f3181,f3182,f3084,f3202,f3203,f3208,f3212,f3213,f3214,f3215,f3105,f3232,f3233,f3238,f3242,f3243,f3244,f3245,f3083,f3300,f3264,f3301,f3272,f3287,f3288,f3291,f3292,f3104,f3376,f3338,f3377,f3347,f3355,f3363,f3364,f3367,f3368,f3398,f3349,f3326,f3276,f3216,f3209,f3199,f3097,f3081,f3109,f3096,f3080,f24]) ).
fof(f24,axiom,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f1586,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1549,f1429]) ).
fof(f1549,plain,
( ! [X0] : inverse(sk_c7) = multiply(multiply(sk_c8,inverse(X0)),X0)
| ~ spl0_1 ),
inference(superposition,[],[f1429,f302]) ).
fof(f1879,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1792,f189]) ).
fof(f1792,plain,
( inverse(sk_c7) = multiply(inverse(identity),sk_c8)
| ~ spl0_1 ),
inference(superposition,[],[f1314,f384]) ).
fof(f1445,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1392,f1308]) ).
fof(f1392,plain,
( ! [X0] : inverse(sk_c7) = multiply(multiply(sk_c8,X0),inverse(X0))
| ~ spl0_1 ),
inference(superposition,[],[f1308,f302]) ).
fof(f2003,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1217,f1308]) ).
fof(f1217,plain,
( ! [X0] : inverse(sk_c7) = multiply(multiply(sk_c8,X0),inverse(X0))
| ~ spl0_1 ),
inference(superposition,[],[f1186,f292]) ).
fof(f812,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f740,f40]) ).
fof(f2427,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f747,f718]) ).
fof(f747,plain,
( multiply(sk_c8,identity) = inverse(sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f718,f302]) ).
fof(f2426,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f762,f718]) ).
fof(f762,plain,
( multiply(sk_c8,identity) = inverse(sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f302,f718]) ).
fof(f2149,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1
| ~ spl0_8 ),
inference(superposition,[],[f2122,f2145]) ).
fof(f752,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f294,f718]) ).
fof(f737,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f718,f294]) ).
fof(f3096,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f2,f736]) ).
fof(f3109,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3100,f740]) ).
fof(f3100,plain,
( identity = multiply(inverse(inverse(sk_c1)),sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f627,f736]) ).
fof(f3081,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f719,f44]) ).
fof(f3097,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f60,f736]) ).
fof(f3199,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f3084,f1]) ).
fof(f3218,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3201,f1144]) ).
fof(f3201,plain,
( multiply(sk_c1,sk_c2) = inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f3084,f189]) ).
fof(f3221,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3205,f3084]) ).
fof(f3205,plain,
( inverse(sk_c7) = multiply(multiply(sk_c8,sk_c1),sk_c2)
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f3084,f302]) ).
fof(f3209,plain,
( ! [X0] : multiply(X0,multiply(sk_c1,sk_c2)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f3084,f3]) ).
fof(f3216,plain,
( ! [X0] : multiply(X0,multiply(sk_c1,sk_c2)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f3,f3084]) ).
fof(f3251,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3235,f3105]) ).
fof(f3235,plain,
( inverse(sk_c7) = multiply(multiply(sk_c8,sk_c2),sk_c1)
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f3105,f302]) ).
fof(f3270,plain,
( sk_c1 = multiply(sk_c8,inverse(multiply(sk_c2,inverse(sk_c7))))
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f3083,f302]) ).
fof(f3276,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1429,f3083]) ).
fof(f3279,plain,
( sk_c1 = multiply(sk_c8,inverse(multiply(sk_c2,inverse(sk_c7))))
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f302,f3083]) ).
fof(f3282,plain,
( inverse(multiply(sk_c2,sk_c8)) = multiply(sk_c7,sk_c1)
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f292,f3083]) ).
fof(f3326,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3284,f740]) ).
fof(f3284,plain,
( ! [X0] : multiply(sk_c1,inverse(inverse(multiply(sk_c2,X0)))) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1308,f3083]) ).
fof(f3345,plain,
( sk_c2 = multiply(sk_c8,inverse(multiply(sk_c1,inverse(sk_c7))))
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f3104,f302]) ).
fof(f3349,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f858,f3104]) ).
fof(f3354,plain,
( sk_c2 = multiply(sk_c8,inverse(multiply(sk_c1,inverse(sk_c7))))
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f302,f3104]) ).
fof(f3398,plain,
( sk_c1 = multiply(inverse(multiply(sk_c1,sk_c2)),sk_c1)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3356,f736]) ).
fof(f3356,plain,
( sk_c1 = multiply(inverse(multiply(sk_c1,sk_c2)),inverse(sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f3083,f3104]) ).
fof(f3358,plain,
( inverse(multiply(sk_c1,sk_c8)) = multiply(sk_c7,sk_c2)
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f292,f3104]) ).
fof(f3368,plain,
( ! [X0,X1] : sk_c2 = multiply(X0,multiply(X1,inverse(multiply(sk_c1,multiply(X0,X1)))))
| ~ spl0_2 ),
inference(superposition,[],[f3,f3104]) ).
fof(f3367,plain,
( ! [X0] : multiply(X0,sk_c2) = inverse(multiply(sk_c1,inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f719,f3104]) ).
fof(f3364,plain,
( ! [X0,X1] : multiply(sk_c2,X1) = multiply(X0,multiply(inverse(multiply(sk_c1,X0)),X1))
| ~ spl0_2 ),
inference(superposition,[],[f3,f3104]) ).
fof(f3363,plain,
( ! [X0] : inverse(multiply(sk_c1,X0)) = multiply(inverse(X0),sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f60,f3104]) ).
fof(f3355,plain,
( multiply(sk_c2,sk_c2) = inverse(multiply(sk_c1,sk_c1))
| ~ spl0_2 ),
inference(superposition,[],[f3076,f3104]) ).
fof(f3347,plain,
( ! [X0,X1] : sk_c2 = multiply(X0,multiply(X1,inverse(multiply(sk_c1,multiply(X0,X1)))))
| ~ spl0_2 ),
inference(superposition,[],[f3104,f3]) ).
fof(f3377,plain,
( sk_c2 = multiply(inverse(multiply(sk_c1,sk_c1)),sk_c1)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3339,f736]) ).
fof(f3339,plain,
( sk_c2 = multiply(inverse(multiply(sk_c1,sk_c1)),inverse(sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f3104,f3104]) ).
fof(f3338,plain,
( ! [X0] : sk_c2 = multiply(inverse(multiply(inverse(X0),sk_c1)),inverse(X0))
| ~ spl0_2 ),
inference(superposition,[],[f3104,f1190]) ).
fof(f3376,plain,
( ! [X0] : sk_c2 = multiply(inverse(multiply(X0,sk_c1)),X0)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3337,f740]) ).
fof(f3337,plain,
( ! [X0] : sk_c2 = multiply(inverse(multiply(X0,sk_c1)),inverse(inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f3104,f1186]) ).
fof(f3104,plain,
( ! [X0] : sk_c2 = multiply(X0,inverse(multiply(sk_c1,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1190,f736]) ).
fof(f3292,plain,
( ! [X0,X1] : sk_c1 = multiply(X0,multiply(X1,inverse(multiply(sk_c2,multiply(X0,X1)))))
| ~ spl0_2 ),
inference(superposition,[],[f3,f3083]) ).
fof(f3291,plain,
( ! [X0] : multiply(X0,sk_c1) = inverse(multiply(sk_c2,inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f719,f3083]) ).
fof(f3288,plain,
( ! [X0,X1] : multiply(sk_c1,X1) = multiply(X0,multiply(inverse(multiply(sk_c2,X0)),X1))
| ~ spl0_2 ),
inference(superposition,[],[f3,f3083]) ).
fof(f3287,plain,
( ! [X0] : inverse(multiply(sk_c2,X0)) = multiply(inverse(X0),sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f60,f3083]) ).
fof(f3272,plain,
( ! [X0,X1] : sk_c1 = multiply(X0,multiply(X1,inverse(multiply(sk_c2,multiply(X0,X1)))))
| ~ spl0_2 ),
inference(superposition,[],[f3083,f3]) ).
fof(f3301,plain,
( sk_c1 = multiply(inverse(multiply(sk_c2,sk_c2)),sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3265,f44]) ).
fof(f3265,plain,
( sk_c1 = multiply(inverse(multiply(sk_c2,sk_c2)),inverse(sk_c1))
| ~ spl0_2 ),
inference(superposition,[],[f3083,f3083]) ).
fof(f3264,plain,
( ! [X0] : sk_c1 = multiply(inverse(multiply(inverse(X0),sk_c2)),inverse(X0))
| ~ spl0_2 ),
inference(superposition,[],[f3083,f1190]) ).
fof(f3300,plain,
( ! [X0] : sk_c1 = multiply(inverse(multiply(X0,sk_c2)),X0)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3263,f740]) ).
fof(f3263,plain,
( ! [X0] : sk_c1 = multiply(inverse(multiply(X0,sk_c2)),inverse(inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f3083,f1186]) ).
fof(f3083,plain,
( ! [X0] : sk_c1 = multiply(X0,inverse(multiply(sk_c2,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1190,f44]) ).
fof(f3245,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,sk_c2),multiply(sk_c1,X1))
| ~ spl0_2 ),
inference(superposition,[],[f3,f3105]) ).
fof(f3244,plain,
( ! [X0] : sk_c1 = multiply(inverse(multiply(X0,sk_c2)),X0)
| ~ spl0_2 ),
inference(superposition,[],[f60,f3105]) ).
fof(f3243,plain,
( ! [X0] : identity = multiply(multiply(X0,sk_c2),multiply(sk_c1,inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f858,f3105]) ).
fof(f3242,plain,
( ! [X0] : multiply(sk_c1,inverse(X0)) = inverse(multiply(X0,sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f1186,f3105]) ).
fof(f3238,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,multiply(X1,sk_c2)),sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f3105,f3]) ).
fof(f3233,plain,
( ! [X0] : multiply(X0,sk_c1) = inverse(multiply(sk_c2,inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f3105,f1691]) ).
fof(f3232,plain,
( ! [X0] : inverse(multiply(sk_c2,X0)) = multiply(inverse(X0),sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f3105,f1314]) ).
fof(f3105,plain,
( ! [X0] : multiply(multiply(X0,sk_c2),sk_c1) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1308,f736]) ).
fof(f3215,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,sk_c1),multiply(sk_c2,X1))
| ~ spl0_2 ),
inference(superposition,[],[f3,f3084]) ).
fof(f3214,plain,
( ! [X0] : sk_c2 = multiply(inverse(multiply(X0,sk_c1)),X0)
| ~ spl0_2 ),
inference(superposition,[],[f60,f3084]) ).
fof(f3213,plain,
( ! [X0] : identity = multiply(multiply(X0,sk_c1),multiply(sk_c2,inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f858,f3084]) ).
fof(f3212,plain,
( ! [X0] : inverse(multiply(X0,sk_c1)) = multiply(sk_c2,inverse(X0))
| ~ spl0_2 ),
inference(superposition,[],[f1186,f3084]) ).
fof(f3208,plain,
( ! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,multiply(X1,sk_c1)),sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f3084,f3]) ).
fof(f3203,plain,
( ! [X0] : multiply(X0,sk_c2) = inverse(multiply(sk_c1,inverse(X0)))
| ~ spl0_2 ),
inference(superposition,[],[f3084,f1691]) ).
fof(f3202,plain,
( ! [X0] : inverse(multiply(sk_c1,X0)) = multiply(inverse(X0),sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f3084,f1314]) ).
fof(f3084,plain,
( ! [X0] : multiply(multiply(X0,sk_c1),sk_c2) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1308,f44]) ).
fof(f3182,plain,
( ! [X0] : sk_c2 = multiply(X0,inverse(multiply(sk_c1,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f3076]) ).
fof(f3181,plain,
( ! [X0] : inverse(multiply(sk_c1,X0)) = multiply(inverse(X0),sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f1314,f3076]) ).
fof(f3177,plain,
( ! [X0] : multiply(sk_c2,X0) = inverse(multiply(inverse(X0),sk_c1))
| ~ spl0_2 ),
inference(superposition,[],[f3076,f1190]) ).
fof(f3176,plain,
( ! [X0] : inverse(multiply(X0,sk_c1)) = multiply(sk_c2,inverse(X0))
| ~ spl0_2 ),
inference(superposition,[],[f3076,f1186]) ).
fof(f3076,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c1,X0)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f60,f44]) ).
fof(f3137,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c1,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3129,f1]) ).
fof(f3129,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(sk_c1,X0))
| ~ spl0_2 ),
inference(superposition,[],[f3,f3075]) ).
fof(f3075,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f2,f44]) ).
fof(f3107,plain,
( ! [X0] : sk_c2 = multiply(inverse(multiply(X0,sk_c1)),X0)
| ~ spl0_2 ),
inference(superposition,[],[f1691,f736]) ).
fof(f3106,plain,
( ! [X0] : multiply(multiply(X0,sk_c1),sk_c2) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1429,f736]) ).
fof(f3102,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c1,X0)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f719,f736]) ).
fof(f3101,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f715,f736]) ).
fof(f736,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f718,f200]) ).
fof(f3086,plain,
( ! [X0] : sk_c1 = multiply(inverse(multiply(X0,sk_c2)),X0)
| ~ spl0_2 ),
inference(superposition,[],[f1691,f44]) ).
fof(f3085,plain,
( ! [X0] : multiply(multiply(X0,sk_c2),sk_c1) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1429,f44]) ).
fof(f3082,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f740,f44]) ).
fof(f3087,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f3079,f740]) ).
fof(f3079,plain,
( identity = multiply(inverse(inverse(sk_c2)),sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f627,f44]) ).
fof(f3078,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(inverse(sk_c2),X0)
| ~ spl0_2 ),
inference(superposition,[],[f199,f44]) ).
fof(f3077,plain,
( sk_c1 = multiply(inverse(sk_c2),identity)
| ~ spl0_2 ),
inference(superposition,[],[f190,f44]) ).
fof(f44,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f42,plain,
( spl0_2
<=> sk_c2 = inverse(sk_c1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f2041,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f754,f740]) ).
fof(f754,plain,
( sk_c1 = inverse(inverse(inverse(sk_c2)))
| ~ spl0_2 ),
inference(superposition,[],[f306,f718]) ).
fof(f1873,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1789,f189]) ).
fof(f1789,plain,
( inverse(sk_c2) = multiply(inverse(identity),sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f1314,f360]) ).
fof(f2034,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f864,f361]) ).
fof(f864,plain,
( multiply(sk_c1,identity) = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f362,f715]) ).
fof(f1583,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1548,f1429]) ).
fof(f1548,plain,
( ! [X0] : inverse(sk_c2) = multiply(multiply(sk_c1,inverse(X0)),X0)
| ~ spl0_2 ),
inference(superposition,[],[f1429,f196]) ).
fof(f2019,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f2018,f361]) ).
fof(f2018,plain,
( multiply(sk_c1,identity) = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1032,f1186]) ).
fof(f1032,plain,
( ! [X0] : multiply(sk_c1,identity) = multiply(X0,inverse(multiply(sk_c2,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f362,f858]) ).
fof(f1442,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1391,f1308]) ).
fof(f1391,plain,
( ! [X0] : inverse(sk_c2) = multiply(multiply(sk_c1,X0),inverse(X0))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f196]) ).
fof(f2044,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f739,f740]) ).
fof(f739,plain,
( sk_c1 = inverse(inverse(inverse(sk_c2)))
| ~ spl0_2 ),
inference(superposition,[],[f718,f306]) ).
fof(f2006,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1214,f1308]) ).
fof(f1214,plain,
( ! [X0] : inverse(sk_c2) = multiply(multiply(sk_c1,X0),inverse(X0))
| ~ spl0_2 ),
inference(superposition,[],[f1186,f63]) ).
fof(f5,axiom,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f1144,plain,
( identity = inverse(identity)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1010,f293]) ).
fof(f1010,plain,
( identity = inverse(multiply(sk_c7,sk_c8))
| ~ spl0_1 ),
inference(superposition,[],[f858,f292]) ).
fof(f1002,plain,
( ! [X0] : identity = multiply(X0,multiply(sk_c8,inverse(multiply(X0,inverse(sk_c7)))))
| ~ spl0_1 ),
inference(superposition,[],[f858,f302]) ).
fof(f1234,plain,
( ! [X0] : inverse(X0) = multiply(sk_c8,inverse(multiply(X0,inverse(sk_c7))))
| ~ spl0_1 ),
inference(superposition,[],[f1186,f302]) ).
fof(f1242,plain,
( ! [X0] : inverse(X0) = multiply(sk_c8,inverse(multiply(X0,inverse(sk_c7))))
| ~ spl0_1 ),
inference(superposition,[],[f302,f1186]) ).
fof(f1627,plain,
( ! [X0] : multiply(sk_c8,inverse(multiply(inverse(X0),inverse(sk_c7)))) = X0
| ~ spl0_1 ),
inference(superposition,[],[f1190,f302]) ).
fof(f1637,plain,
( ! [X0] : multiply(sk_c8,inverse(multiply(inverse(X0),inverse(sk_c7)))) = X0
| ~ spl0_1 ),
inference(superposition,[],[f302,f1190]) ).
fof(f1758,plain,
( ! [X0] : inverse(X0) = multiply(inverse(multiply(sk_c8,X0)),inverse(sk_c7))
| ~ spl0_1 ),
inference(superposition,[],[f1314,f302]) ).
fof(f2424,plain,
( identity = inverse(identity)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2423,f715]) ).
fof(f2423,plain,
( inverse(identity) = multiply(sk_c7,inverse(sk_c7))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1765,f40]) ).
fof(f1765,plain,
( inverse(identity) = multiply(inverse(sk_c8),inverse(sk_c7))
| ~ spl0_1 ),
inference(superposition,[],[f1314,f294]) ).
fof(f1903,plain,
( ! [X0] : multiply(inverse(multiply(sk_c8,inverse(X0))),inverse(sk_c7)) = X0
| ~ spl0_1 ),
inference(superposition,[],[f1691,f302]) ).
fof(f1621,plain,
( inverse(sk_c7) = multiply(sk_c8,inverse(identity))
| ~ spl0_1 ),
inference(superposition,[],[f1190,f300]) ).
fof(f1398,plain,
( inverse(sk_c7) = multiply(sk_c8,inverse(identity))
| ~ spl0_1 ),
inference(superposition,[],[f1308,f294]) ).
fof(f1997,plain,
( inverse(sk_c7) = multiply(sk_c8,inverse(identity))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1227,f740]) ).
fof(f1227,plain,
( inverse(inverse(inverse(sk_c7))) = multiply(sk_c8,inverse(identity))
| ~ spl0_1 ),
inference(superposition,[],[f1186,f300]) ).
fof(f1226,plain,
( inverse(sk_c7) = multiply(sk_c8,inverse(identity))
| ~ spl0_1 ),
inference(superposition,[],[f1186,f293]) ).
fof(f1158,plain,
( identity = inverse(identity)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1024,f293]) ).
fof(f1024,plain,
( identity = inverse(multiply(sk_c7,sk_c8))
| ~ spl0_1 ),
inference(superposition,[],[f292,f858]) ).
fof(f1843,plain,
( identity = inverse(identity)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1773,f2]) ).
fof(f1773,plain,
( inverse(identity) = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f1314,f395]) ).
fof(f692,plain,
identity = inverse(identity),
inference(superposition,[],[f627,f190]) ).
fof(f695,plain,
identity = inverse(identity),
inference(superposition,[],[f190,f627]) ).
fof(f743,plain,
identity = inverse(identity),
inference(superposition,[],[f718,f2]) ).
fof(f744,plain,
identity = inverse(identity),
inference(superposition,[],[f718,f189]) ).
fof(f758,plain,
identity = inverse(identity),
inference(superposition,[],[f2,f718]) ).
fof(f759,plain,
identity = inverse(identity),
inference(superposition,[],[f189,f718]) ).
fof(f852,plain,
identity = inverse(identity),
inference(superposition,[],[f715,f1]) ).
fof(f859,plain,
identity = inverse(identity),
inference(superposition,[],[f1,f715]) ).
fof(f2040,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f760,f740]) ).
fof(f760,plain,
identity = inverse(inverse(inverse(identity))),
inference(superposition,[],[f627,f718]) ).
fof(f2043,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f745,f740]) ).
fof(f745,plain,
identity = inverse(inverse(inverse(identity))),
inference(superposition,[],[f718,f627]) ).
fof(f1145,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1011,f2]) ).
fof(f1011,plain,
! [X0] : identity = inverse(multiply(inverse(X0),X0)),
inference(superposition,[],[f858,f60]) ).
fof(f1146,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1012,f715]) ).
fof(f1012,plain,
! [X0] : identity = inverse(multiply(X0,inverse(X0))),
inference(superposition,[],[f858,f719]) ).
fof(f1159,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1025,f2]) ).
fof(f1025,plain,
! [X0] : identity = inverse(multiply(inverse(X0),X0)),
inference(superposition,[],[f60,f858]) ).
fof(f1160,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1026,f715]) ).
fof(f1026,plain,
! [X0] : identity = inverse(multiply(X0,inverse(X0))),
inference(superposition,[],[f719,f858]) ).
fof(f1255,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1192,f715]) ).
fof(f1192,plain,
! [X0] : inverse(identity) = multiply(X0,inverse(X0)),
inference(superposition,[],[f1186,f1]) ).
fof(f1440,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1389,f715]) ).
fof(f1389,plain,
! [X0] : inverse(identity) = multiply(X0,inverse(X0)),
inference(superposition,[],[f1308,f189]) ).
fof(f1837,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1768,f715]) ).
fof(f1768,plain,
! [X0] : inverse(identity) = multiply(inverse(X0),inverse(inverse(X0))),
inference(superposition,[],[f1314,f190]) ).
fof(f1975,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1763,f2]) ).
fof(f1763,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[],[f1314,f718]) ).
fof(f1983,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f1546,f2]) ).
fof(f1546,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[],[f1429,f189]) ).
fof(f1996,plain,
( sk_c7 = multiply(sk_c7,inverse(identity))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1228,f40]) ).
fof(f1228,plain,
( inverse(sk_c8) = multiply(sk_c7,inverse(identity))
| ~ spl0_1 ),
inference(superposition,[],[f1186,f384]) ).
fof(f1406,plain,
( sk_c7 = multiply(sk_c7,inverse(identity))
| ~ spl0_1 ),
inference(superposition,[],[f1308,f395]) ).
fof(f2145,plain,
( sk_c7 = sk_c5
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2144,f395]) ).
fof(f2144,plain,
( sk_c5 = multiply(sk_c7,identity)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2134,f40]) ).
fof(f2134,plain,
( sk_c5 = multiply(inverse(sk_c8),identity)
| ~ spl0_8 ),
inference(superposition,[],[f190,f2122]) ).
fof(f2143,plain,
( ! [X0] : sk_c5 = multiply(inverse(multiply(X0,sk_c8)),X0)
| ~ spl0_8 ),
inference(superposition,[],[f1691,f2122]) ).
fof(f2142,plain,
( ! [X0] : multiply(multiply(X0,sk_c8),sk_c5) = X0
| ~ spl0_8 ),
inference(superposition,[],[f1429,f2122]) ).
fof(f2141,plain,
( ! [X0] : multiply(multiply(X0,sk_c5),sk_c8) = X0
| ~ spl0_8 ),
inference(superposition,[],[f1308,f2122]) ).
fof(f2140,plain,
( ! [X0] : sk_c5 = multiply(X0,inverse(multiply(sk_c8,X0)))
| ~ spl0_8 ),
inference(superposition,[],[f1190,f2122]) ).
fof(f2148,plain,
( sk_c7 = sk_c5
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2139,f40]) ).
fof(f2139,plain,
( inverse(sk_c8) = sk_c5
| ~ spl0_8 ),
inference(superposition,[],[f740,f2122]) ).
fof(f2138,plain,
( ! [X0] : multiply(sk_c5,multiply(sk_c8,X0)) = X0
| ~ spl0_8 ),
inference(superposition,[],[f719,f2122]) ).
fof(f2137,plain,
( identity = multiply(sk_c5,sk_c8)
| ~ spl0_8 ),
inference(superposition,[],[f715,f2122]) ).
fof(f2147,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2136,f740]) ).
fof(f2136,plain,
( identity = multiply(inverse(inverse(sk_c8)),sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f627,f2122]) ).
fof(f2146,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,X0)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2135,f40]) ).
fof(f2135,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = multiply(sk_c5,X0)
| ~ spl0_8 ),
inference(superposition,[],[f199,f2122]) ).
fof(f2133,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c5,X0)) = X0
| ~ spl0_8 ),
inference(superposition,[],[f60,f2122]) ).
fof(f2132,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f2,f2122]) ).
fof(f2122,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f2120]) ).
fof(f2120,plain,
( spl0_8
<=> sk_c8 = inverse(sk_c5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f15,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f13,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f14,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c6 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f8,axiom,
( sk_c6 = multiply(sk_c5,sk_c8)
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f7,axiom,
( sk_c7 = multiply(sk_c8,sk_c6)
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f9,axiom,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f2062,plain,
( identity = sk_c8
| sk_c8 = inverse(sk_c5)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f9,f360]) ).
fof(f1140,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1006,f360]) ).
fof(f1006,plain,
( identity = inverse(multiply(sk_c1,sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f858,f362]) ).
fof(f2096,plain,
( ! [X0] : sk_c2 = multiply(inverse(multiply(X0,sk_c1)),X0)
| ~ spl0_2 ),
inference(superposition,[],[f1691,f736]) ).
fof(f2095,plain,
( ! [X0] : multiply(multiply(X0,sk_c1),sk_c2) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1429,f736]) ).
fof(f2094,plain,
( ! [X0] : multiply(multiply(X0,sk_c2),sk_c1) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1308,f736]) ).
fof(f2093,plain,
( ! [X0] : sk_c2 = multiply(X0,inverse(multiply(sk_c1,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1190,f736]) ).
fof(f2063,plain,
( identity = sk_c8
| sk_c8 = inverse(sk_c4)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f5,f360]) ).
fof(f21,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f2059,plain,
( identity = sk_c8
| sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f6,f360]) ).
fof(f624,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f190,f306]) ).
fof(f626,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f306,f190]) ).
fof(f2052,plain,
( identity = sk_c8
| sk_c7 = multiply(sk_c8,sk_c6)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f7,f360]) ).
fof(f2051,plain,
( identity = sk_c8
| sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f8,f360]) ).
fof(f20,axiom,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f2042,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f746,f361]) ).
fof(f746,plain,
( multiply(sk_c1,identity) = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f718,f196]) ).
fof(f751,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f200,f718]) ).
fof(f2039,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f761,f361]) ).
fof(f761,plain,
( multiply(sk_c1,identity) = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f196,f718]) ).
fof(f811,plain,
( sk_c1 = inverse(sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f740,f44]) ).
fof(f2036,plain,
( ! [X3,X8,X6,X5] :
( identity != sk_c8
| sk_c8 != inverse(X8)
| sk_c8 != inverse(X5)
| sk_c8 != inverse(X6)
| sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f831,f715]) ).
fof(f831,plain,
( ! [X3,X8,X6,X5] :
( sk_c8 != inverse(X8)
| sk_c8 != inverse(X5)
| sk_c8 != inverse(X6)
| sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1 ),
inference(subsumption_resolution,[],[f36,f40]) ).
fof(f962,plain,
! [X0] : identity = multiply(inverse(X0),multiply(X0,inverse(identity))),
inference(superposition,[],[f858,f2]) ).
fof(f2032,plain,
! [X0] : identity = multiply(inverse(X0),multiply(X0,inverse(identity))),
inference(forward_demodulation,[],[f964,f740]) ).
fof(f964,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),multiply(X0,inverse(identity))),
inference(superposition,[],[f858,f627]) ).
fof(f1097,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),inverse(identity)))),
inference(forward_demodulation,[],[f989,f3]) ).
fof(f989,plain,
! [X0,X1] : identity = multiply(X0,multiply(multiply(X1,inverse(multiply(X0,X1))),inverse(identity))),
inference(superposition,[],[f858,f858]) ).
fof(f990,plain,
! [X0] : identity = multiply(X0,multiply(inverse(X0),inverse(identity))),
inference(superposition,[],[f858,f715]) ).
fof(f991,plain,
( identity = multiply(sk_c2,multiply(sk_c1,inverse(identity)))
| ~ spl0_2 ),
inference(superposition,[],[f858,f46]) ).
fof(f2024,plain,
( identity = multiply(sk_c2,multiply(sk_c1,inverse(identity)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f992,f740]) ).
fof(f992,plain,
( identity = multiply(inverse(inverse(sk_c2)),multiply(sk_c1,inverse(identity)))
| ~ spl0_2 ),
inference(superposition,[],[f858,f297]) ).
fof(f993,plain,
( identity = multiply(sk_c1,multiply(sk_c2,inverse(identity)))
| ~ spl0_2 ),
inference(superposition,[],[f858,f360]) ).
fof(f994,plain,
( identity = multiply(sk_c7,multiply(sk_c8,inverse(identity)))
| ~ spl0_1 ),
inference(superposition,[],[f858,f293]) ).
fof(f2023,plain,
( identity = multiply(sk_c7,multiply(sk_c8,inverse(identity)))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f995,f740]) ).
fof(f995,plain,
( identity = multiply(inverse(inverse(sk_c7)),multiply(sk_c8,inverse(identity)))
| ~ spl0_1 ),
inference(superposition,[],[f858,f300]) ).
fof(f996,plain,
( identity = multiply(sk_c8,multiply(sk_c7,inverse(identity)))
| ~ spl0_1 ),
inference(superposition,[],[f858,f384]) ).
fof(f1000,plain,
! [X0] : identity = multiply(X0,inverse(multiply(X0,inverse(identity)))),
inference(superposition,[],[f858,f189]) ).
fof(f1001,plain,
( ! [X0] : identity = multiply(X0,multiply(sk_c1,inverse(multiply(X0,inverse(sk_c2)))))
| ~ spl0_2 ),
inference(superposition,[],[f858,f196]) ).
fof(f1141,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1007,f46]) ).
fof(f1007,plain,
( identity = inverse(multiply(sk_c2,sk_c1))
| ~ spl0_2 ),
inference(superposition,[],[f858,f63]) ).
fof(f1154,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1020,f360]) ).
fof(f1020,plain,
( identity = inverse(multiply(sk_c1,sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f362,f858]) ).
fof(f1155,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1021,f46]) ).
fof(f1021,plain,
( identity = inverse(multiply(sk_c2,sk_c1))
| ~ spl0_2 ),
inference(superposition,[],[f63,f858]) ).
fof(f2010,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(forward_demodulation,[],[f1193,f740]) ).
fof(f1193,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(identity)),
inference(superposition,[],[f1186,f2]) ).
fof(f2009,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(forward_demodulation,[],[f2008,f740]) ).
fof(f2008,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(identity)),
inference(forward_demodulation,[],[f1195,f740]) ).
fof(f1195,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = multiply(X0,inverse(identity)),
inference(superposition,[],[f1186,f627]) ).
fof(f2002,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),inverse(identity)),
inference(forward_demodulation,[],[f1220,f1186]) ).
fof(f1220,plain,
! [X0,X1] : inverse(X0) = multiply(multiply(X1,inverse(multiply(X0,X1))),inverse(identity)),
inference(superposition,[],[f1186,f858]) ).
fof(f1221,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),inverse(identity)),
inference(superposition,[],[f1186,f715]) ).
fof(f1223,plain,
( inverse(sk_c2) = multiply(sk_c1,inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f1186,f46]) ).
fof(f2001,plain,
( inverse(sk_c2) = multiply(sk_c1,inverse(identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1224,f740]) ).
fof(f1224,plain,
( inverse(inverse(inverse(sk_c2))) = multiply(sk_c1,inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f1186,f297]) ).
fof(f2000,plain,
( sk_c2 = multiply(sk_c2,inverse(identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1225,f44]) ).
fof(f1225,plain,
( inverse(sk_c1) = multiply(sk_c2,inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f1186,f360]) ).
fof(f1232,plain,
! [X0] : inverse(X0) = inverse(multiply(X0,inverse(identity))),
inference(superposition,[],[f1186,f189]) ).
fof(f1233,plain,
( ! [X0] : inverse(X0) = multiply(sk_c1,inverse(multiply(X0,inverse(sk_c2))))
| ~ spl0_2 ),
inference(superposition,[],[f1186,f196]) ).
fof(f1240,plain,
! [X0] : inverse(X0) = inverse(multiply(X0,inverse(identity))),
inference(superposition,[],[f189,f1186]) ).
fof(f1241,plain,
( ! [X0] : inverse(X0) = multiply(sk_c1,inverse(multiply(X0,inverse(sk_c2))))
| ~ spl0_2 ),
inference(superposition,[],[f196,f1186]) ).
fof(f1243,plain,
( ! [X0] : inverse(multiply(X0,sk_c1)) = multiply(sk_c2,inverse(X0))
| ~ spl0_2 ),
inference(superposition,[],[f63,f1186]) ).
fof(f1244,plain,
( ! [X0] : multiply(sk_c1,inverse(X0)) = inverse(multiply(X0,sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f362,f1186]) ).
fof(f1245,plain,
( ! [X0] : inverse(multiply(X0,sk_c8)) = multiply(sk_c7,inverse(X0))
| ~ spl0_1 ),
inference(superposition,[],[f292,f1186]) ).
fof(f1396,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(superposition,[],[f1308,f718]) ).
fof(f1397,plain,
( inverse(sk_c2) = multiply(sk_c1,inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f200]) ).
fof(f1987,plain,
( inverse(sk_c2) = multiply(sk_c1,inverse(identity))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1400,f740]) ).
fof(f1400,plain,
( inverse(inverse(inverse(sk_c2))) = multiply(sk_c1,inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f306]) ).
fof(f1986,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(forward_demodulation,[],[f1401,f740]) ).
fof(f1401,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(identity)),
inference(superposition,[],[f1308,f190]) ).
fof(f1402,plain,
( sk_c1 = multiply(sk_c1,inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f361]) ).
fof(f1403,plain,
( sk_c2 = multiply(sk_c2,inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f369]) ).
fof(f1408,plain,
( ! [X0] : sk_c1 = multiply(X0,inverse(multiply(sk_c2,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f362]) ).
fof(f1409,plain,
( ! [X0] : sk_c2 = multiply(X0,inverse(multiply(sk_c1,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f63]) ).
fof(f1421,plain,
( sk_c1 = multiply(identity,inverse(sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f1308,f360]) ).
fof(f1430,plain,
( ! [X0] : multiply(multiply(X0,sk_c1),sk_c2) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1308,f44]) ).
fof(f1538,plain,
( ! [X0] : multiply(multiply(X0,sk_c2),sk_c1) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1429,f44]) ).
fof(f1555,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(superposition,[],[f1429,f718]) ).
fof(f1561,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(superposition,[],[f718,f1429]) ).
fof(f1598,plain,
( ! [X0] : sk_c1 = multiply(X0,inverse(multiply(sk_c2,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1190,f44]) ).
fof(f1602,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(superposition,[],[f1190,f2]) ).
fof(f1981,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(forward_demodulation,[],[f1604,f740]) ).
fof(f1604,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,inverse(identity)),
inference(superposition,[],[f1190,f627]) ).
fof(f1605,plain,
( ! [X0] : sk_c2 = multiply(X0,inverse(multiply(sk_c1,X0)))
| ~ spl0_2 ),
inference(superposition,[],[f1190,f196]) ).
fof(f1980,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(forward_demodulation,[],[f1979,f740]) ).
fof(f1979,plain,
! [X0] : multiply(inverse(inverse(X0)),inverse(identity)) = X0,
inference(forward_demodulation,[],[f1616,f1186]) ).
fof(f1616,plain,
! [X0,X1] : multiply(multiply(X1,inverse(multiply(inverse(X0),X1))),inverse(identity)) = X0,
inference(superposition,[],[f1190,f858]) ).
fof(f1978,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(forward_demodulation,[],[f1617,f740]) ).
fof(f1617,plain,
! [X0] : multiply(inverse(inverse(X0)),inverse(identity)) = X0,
inference(superposition,[],[f1190,f715]) ).
fof(f1620,plain,
( inverse(sk_c2) = multiply(sk_c1,inverse(identity))
| ~ spl0_2 ),
inference(superposition,[],[f1190,f297]) ).
fof(f1625,plain,
! [X0] : inverse(multiply(inverse(X0),inverse(identity))) = X0,
inference(superposition,[],[f1190,f189]) ).
fof(f1626,plain,
( ! [X0] : multiply(sk_c1,inverse(multiply(inverse(X0),inverse(sk_c2)))) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1190,f196]) ).
fof(f1635,plain,
! [X0] : inverse(multiply(inverse(X0),inverse(identity))) = X0,
inference(superposition,[],[f189,f1190]) ).
fof(f1636,plain,
( ! [X0] : multiply(sk_c1,inverse(multiply(inverse(X0),inverse(sk_c2)))) = X0
| ~ spl0_2 ),
inference(superposition,[],[f196,f1190]) ).
fof(f1638,plain,
( ! [X0] : multiply(sk_c2,X0) = inverse(multiply(inverse(X0),sk_c1))
| ~ spl0_2 ),
inference(superposition,[],[f63,f1190]) ).
fof(f1639,plain,
( ! [X0] : multiply(sk_c1,X0) = inverse(multiply(inverse(X0),sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f362,f1190]) ).
fof(f1640,plain,
( ! [X0] : multiply(sk_c7,X0) = inverse(multiply(inverse(X0),sk_c8))
| ~ spl0_1 ),
inference(superposition,[],[f292,f1190]) ).
fof(f1754,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),inverse(identity)),
inference(superposition,[],[f1314,f189]) ).
fof(f1757,plain,
( ! [X0] : inverse(X0) = multiply(inverse(multiply(sk_c1,X0)),inverse(sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f1314,f196]) ).
fof(f1974,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1973,f715]) ).
fof(f1973,plain,
( inverse(identity) = multiply(sk_c2,inverse(sk_c2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1764,f44]) ).
fof(f1764,plain,
( inverse(identity) = multiply(inverse(sk_c1),inverse(sk_c2))
| ~ spl0_2 ),
inference(superposition,[],[f1314,f200]) ).
fof(f1970,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1969,f715]) ).
fof(f1969,plain,
( inverse(identity) = multiply(sk_c2,inverse(sk_c2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1831,f44]) ).
fof(f1831,plain,
( inverse(identity) = multiply(inverse(sk_c1),inverse(sk_c2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1767,f740]) ).
fof(f1767,plain,
( inverse(identity) = multiply(inverse(sk_c1),inverse(inverse(inverse(sk_c2))))
| ~ spl0_2 ),
inference(superposition,[],[f1314,f306]) ).
fof(f1968,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1769,f2]) ).
fof(f1769,plain,
( multiply(inverse(sk_c1),sk_c1) = inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f1314,f361]) ).
fof(f1840,plain,
( identity = inverse(identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1770,f2]) ).
fof(f1770,plain,
( inverse(identity) = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f1314,f369]) ).
fof(f1775,plain,
( ! [X0] : inverse(multiply(sk_c2,X0)) = multiply(inverse(X0),sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f1314,f362]) ).
fof(f1776,plain,
( ! [X0] : inverse(multiply(sk_c1,X0)) = multiply(inverse(X0),sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f1314,f63]) ).
fof(f1779,plain,
( ! [X0] : inverse(multiply(sk_c8,X0)) = multiply(inverse(X0),sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f1314,f292]) ).
fof(f1889,plain,
( ! [X0] : sk_c1 = multiply(inverse(multiply(X0,sk_c2)),X0)
| ~ spl0_2 ),
inference(superposition,[],[f1691,f44]) ).
fof(f1963,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(forward_demodulation,[],[f1898,f740]) ).
fof(f1898,plain,
! [X0] : multiply(inverse(inverse(X0)),inverse(identity)) = X0,
inference(superposition,[],[f1691,f189]) ).
fof(f1902,plain,
( ! [X0] : multiply(inverse(multiply(sk_c1,inverse(X0))),inverse(sk_c2)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f1691,f196]) ).
fof(f1919,plain,
! [X0,X1] : multiply(X1,X0) = inverse(multiply(inverse(X0),inverse(X1))),
inference(superposition,[],[f1429,f1691]) ).
fof(f1917,plain,
! [X2,X0,X1] : multiply(X1,X2) = multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)),
inference(superposition,[],[f3,f1691]) ).
fof(f1913,plain,
! [X0,X1] : multiply(X1,inverse(X0)) = inverse(multiply(X0,inverse(X1))),
inference(superposition,[],[f1308,f1691]) ).
fof(f1907,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,multiply(X1,inverse(X2)))),multiply(X0,X1)) = X2,
inference(superposition,[],[f1691,f3]) ).
fof(f1691,plain,
! [X0,X1] : multiply(inverse(multiply(X1,inverse(X0))),X1) = X0,
inference(forward_demodulation,[],[f1618,f740]) ).
fof(f1618,plain,
! [X0,X1] : multiply(inverse(multiply(X1,inverse(X0))),inverse(inverse(X1))) = X0,
inference(superposition,[],[f1190,f1186]) ).
fof(f1804,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[],[f1429,f1314]) ).
fof(f1802,plain,
! [X2,X0,X1] : multiply(inverse(X1),X2) = multiply(inverse(multiply(X0,X1)),multiply(X0,X2)),
inference(superposition,[],[f3,f1314]) ).
fof(f1798,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[],[f1308,f1314]) ).
fof(f1781,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[],[f1314,f719]) ).
fof(f1780,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[],[f1314,f60]) ).
fof(f1762,plain,
! [X2,X0,X1] : inverse(X2) = multiply(inverse(multiply(X0,multiply(X1,X2))),multiply(X0,X1)),
inference(superposition,[],[f1314,f3]) ).
fof(f1314,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),X1),
inference(forward_demodulation,[],[f1222,f740]) ).
fof(f1222,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(X1,X0)),inverse(inverse(X1))),
inference(superposition,[],[f1186,f1186]) ).
fof(f1651,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,inverse(multiply(inverse(X2),multiply(X0,X1))))) = X2,
inference(superposition,[],[f3,f1190]) ).
fof(f1650,plain,
! [X0,X1] : multiply(X0,X1) = inverse(multiply(inverse(X1),inverse(X0))),
inference(superposition,[],[f719,f1190]) ).
fof(f1648,plain,
! [X2,X0,X1] : multiply(X1,X2) = multiply(X0,multiply(inverse(multiply(inverse(X1),X0)),X2)),
inference(superposition,[],[f3,f1190]) ).
fof(f1647,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(superposition,[],[f60,f1190]) ).
fof(f1646,plain,
! [X0,X1] : identity = multiply(X0,multiply(inverse(multiply(inverse(X1),X0)),inverse(X1))),
inference(superposition,[],[f858,f1190]) ).
fof(f1645,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(multiply(inverse(X1),X0)),inverse(X1)),
inference(superposition,[],[f1186,f1190]) ).
fof(f1630,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,inverse(multiply(inverse(X2),multiply(X0,X1))))) = X2,
inference(superposition,[],[f1190,f3]) ).
fof(f1619,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(X1),inverse(X0))),inverse(X1)) = X0,
inference(superposition,[],[f1190,f1190]) ).
fof(f1190,plain,
! [X0,X1] : multiply(X1,inverse(multiply(inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f1040,f718]) ).
fof(f1040,plain,
! [X0,X1] : multiply(X0,identity) = multiply(X1,inverse(multiply(inverse(X0),X1))),
inference(superposition,[],[f719,f858]) ).
fof(f1559,plain,
! [X2,X0,X1] : multiply(X0,X2) = multiply(multiply(X0,inverse(X1)),multiply(X1,X2)),
inference(superposition,[],[f3,f1429]) ).
fof(f1558,plain,
! [X0,X1] : multiply(inverse(multiply(X0,inverse(X1))),X0) = X1,
inference(superposition,[],[f60,f1429]) ).
fof(f1557,plain,
! [X0,X1] : identity = multiply(multiply(X0,inverse(X1)),multiply(X1,inverse(X0))),
inference(superposition,[],[f858,f1429]) ).
fof(f1556,plain,
! [X0,X1] : multiply(X1,inverse(X0)) = inverse(multiply(X0,inverse(X1))),
inference(superposition,[],[f1186,f1429]) ).
fof(f1553,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(multiply(X0,multiply(X1,inverse(X2))),X2),
inference(superposition,[],[f1429,f3]) ).
fof(f1429,plain,
! [X0,X1] : multiply(multiply(X1,inverse(X0)),X0) = X1,
inference(superposition,[],[f1308,f740]) ).
fof(f1438,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),multiply(inverse(X1),X2)) = multiply(X0,X2),
inference(superposition,[],[f3,f1308]) ).
fof(f1437,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(superposition,[],[f60,f1308]) ).
fof(f1436,plain,
! [X0,X1] : identity = multiply(multiply(X0,X1),multiply(inverse(X1),inverse(X0))),
inference(superposition,[],[f858,f1308]) ).
fof(f1435,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[],[f1186,f1308]) ).
fof(f1414,plain,
! [X0,X1] : multiply(X1,inverse(multiply(inverse(X0),X1))) = X0,
inference(superposition,[],[f1308,f719]) ).
fof(f1395,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(multiply(X0,multiply(X1,X2)),inverse(X2)),
inference(superposition,[],[f1308,f3]) ).
fof(f1308,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[],[f1218,f740]) ).
fof(f1218,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(multiply(X0,X1),inverse(X1)),
inference(superposition,[],[f1186,f60]) ).
fof(f1254,plain,
! [X2,X0,X1] : inverse(X2) = multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1))))),
inference(superposition,[],[f3,f1186]) ).
fof(f1253,plain,
! [X0,X1] : inverse(multiply(X1,inverse(X0))) = multiply(X0,inverse(X1)),
inference(superposition,[],[f719,f1186]) ).
fof(f1251,plain,
! [X2,X0,X1] : multiply(X0,multiply(inverse(multiply(X1,X0)),X2)) = multiply(inverse(X1),X2),
inference(superposition,[],[f3,f1186]) ).
fof(f1250,plain,
! [X0,X1] : inverse(multiply(X1,X0)) = multiply(inverse(X0),inverse(X1)),
inference(superposition,[],[f60,f1186]) ).
fof(f1385,plain,
! [X0,X1] : identity = multiply(X0,multiply(inverse(multiply(X1,X0)),X1)),
inference(forward_demodulation,[],[f1249,f740]) ).
fof(f1249,plain,
! [X0,X1] : identity = multiply(X0,multiply(inverse(multiply(X1,X0)),inverse(inverse(X1)))),
inference(superposition,[],[f858,f1186]) ).
fof(f1237,plain,
! [X2,X0,X1] : inverse(X2) = multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1))))),
inference(superposition,[],[f1186,f3]) ).
fof(f1219,plain,
! [X0,X1] : inverse(X0) = multiply(multiply(inverse(X0),X1),inverse(X1)),
inference(superposition,[],[f1186,f719]) ).
fof(f1200,plain,
! [X2,X0,X1] : inverse(multiply(X0,X1)) = multiply(X2,inverse(multiply(X0,multiply(X1,X2)))),
inference(superposition,[],[f1186,f3]) ).
fof(f1186,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f1037,f718]) ).
fof(f1037,plain,
! [X0,X1] : multiply(inverse(X0),identity) = multiply(X1,inverse(multiply(X0,X1))),
inference(superposition,[],[f60,f858]) ).
fof(f1191,plain,
! [X2,X0,X1] : identity = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1041,f3]) ).
fof(f1041,plain,
! [X2,X0,X1] : identity = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(multiply(X0,X1),X2))))),
inference(superposition,[],[f3,f858]) ).
fof(f1188,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(forward_demodulation,[],[f1187,f1]) ).
fof(f1187,plain,
! [X2,X0,X1] : multiply(identity,X2) = multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))),
inference(forward_demodulation,[],[f1038,f3]) ).
fof(f1038,plain,
! [X2,X0,X1] : multiply(identity,X2) = multiply(X0,multiply(multiply(X1,inverse(multiply(X0,X1))),X2)),
inference(superposition,[],[f3,f858]) ).
fof(f1153,plain,
! [X2,X0,X1] : identity = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))),
inference(forward_demodulation,[],[f1019,f3]) ).
fof(f1019,plain,
! [X2,X0,X1] : identity = multiply(X0,multiply(X1,multiply(X2,inverse(multiply(multiply(X0,X1),X2))))),
inference(superposition,[],[f858,f3]) ).
fof(f1005,plain,
! [X2,X0,X1] : identity = multiply(X2,multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1)))))),
inference(superposition,[],[f858,f3]) ).
fof(f969,plain,
! [X2,X0,X1] : identity = multiply(multiply(X0,X1),multiply(X2,inverse(multiply(X0,multiply(X1,X2))))),
inference(superposition,[],[f858,f3]) ).
fof(f858,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f715,f3]) ).
fof(f937,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(superposition,[],[f3,f719]) ).
fof(f924,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(superposition,[],[f719,f3]) ).
fof(f719,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f199,f60]) ).
fof(f872,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f3,f715]) ).
fof(f892,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f870,f1]) ).
fof(f870,plain,
! [X0,X1] : multiply(identity,X1) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[],[f3,f715]) ).
fof(f715,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f199,f2]) ).
fof(f826,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f2,f740]) ).
fof(f825,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f60,f740]) ).
fof(f740,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f718,f190]) ).
fof(f808,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f771,f718]) ).
fof(f771,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f199,f718]) ).
fof(f755,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(superposition,[],[f190,f718]) ).
fof(f790,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f749,f718]) ).
fof(f749,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[],[f718,f199]) ).
fof(f718,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f199,f190]) ).
fof(f729,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f60,f199]) ).
fof(f728,plain,
! [X0] : multiply(X0,identity) = X0,
inference(superposition,[],[f190,f199]) ).
fof(f724,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)) = X1,
inference(superposition,[],[f60,f199]) ).
fof(f723,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f2,f199]) ).
fof(f199,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[],[f60,f60]) ).
fof(f707,plain,
! [X0,X1] : multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f694,f1]) ).
fof(f694,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(inverse(inverse(X0))),multiply(X0,X1)),
inference(superposition,[],[f3,f627]) ).
fof(f693,plain,
! [X0] : multiply(inverse(inverse(inverse(inverse(X0)))),identity) = X0,
inference(superposition,[],[f60,f627]) ).
fof(f627,plain,
! [X0] : identity = multiply(inverse(inverse(inverse(X0))),X0),
inference(superposition,[],[f60,f190]) ).
fof(f637,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(forward_demodulation,[],[f628,f1]) ).
fof(f628,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),multiply(identity,X1)),
inference(superposition,[],[f3,f190]) ).
fof(f190,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f60,f2]) ).
fof(f515,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(inverse(inverse(inverse(sk_c2))),X0)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f514,f1]) ).
fof(f514,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(inverse(inverse(inverse(sk_c2))),multiply(identity,X0))
| ~ spl0_2 ),
inference(superposition,[],[f3,f306]) ).
fof(f513,plain,
( identity = multiply(inverse(inverse(inverse(inverse(sk_c2)))),sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f60,f306]) ).
fof(f306,plain,
( sk_c1 = multiply(inverse(inverse(inverse(sk_c2))),identity)
| ~ spl0_2 ),
inference(superposition,[],[f60,f297]) ).
fof(f395,plain,
( sk_c7 = multiply(sk_c7,identity)
| ~ spl0_1 ),
inference(superposition,[],[f292,f384]) ).
fof(f398,plain,
( sk_c7 = multiply(sk_c7,identity)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f396,f40]) ).
fof(f396,plain,
( sk_c7 = multiply(inverse(sk_c8),identity)
| ~ spl0_1 ),
inference(superposition,[],[f60,f384]) ).
fof(f384,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f302,f2]) ).
fof(f389,plain,
( ! [X0] : multiply(inverse(inverse(sk_c7)),multiply(sk_c8,X0)) = X0
| ~ spl0_1 ),
inference(superposition,[],[f60,f302]) ).
fof(f388,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl0_1 ),
inference(superposition,[],[f2,f302]) ).
fof(f302,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c7),X0)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f301,f1]) ).
fof(f301,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c7),multiply(identity,X0))
| ~ spl0_1 ),
inference(superposition,[],[f3,f294]) ).
fof(f362,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f196,f60]) ).
fof(f369,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_2 ),
inference(superposition,[],[f63,f360]) ).
fof(f361,plain,
( sk_c1 = multiply(sk_c1,identity)
| ~ spl0_2 ),
inference(superposition,[],[f196,f200]) ).
fof(f373,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f371,f1]) ).
fof(f371,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c1,multiply(sk_c2,X0))
| ~ spl0_2 ),
inference(superposition,[],[f3,f360]) ).
fof(f372,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f370,f44]) ).
fof(f370,plain,
( sk_c2 = multiply(inverse(sk_c1),identity)
| ~ spl0_2 ),
inference(superposition,[],[f60,f360]) ).
fof(f360,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f196,f2]) ).
fof(f367,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f60,f196]) ).
fof(f366,plain,
( sk_c1 = multiply(sk_c1,identity)
| ~ spl0_2 ),
inference(superposition,[],[f200,f196]) ).
fof(f364,plain,
( ! [X0] : multiply(inverse(inverse(sk_c2)),multiply(sk_c1,X0)) = X0
| ~ spl0_2 ),
inference(superposition,[],[f60,f196]) ).
fof(f363,plain,
( identity = multiply(sk_c1,sk_c2)
| ~ spl0_2 ),
inference(superposition,[],[f2,f196]) ).
fof(f196,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(inverse(sk_c2),X0)
| ~ spl0_2 ),
inference(superposition,[],[f60,f63]) ).
fof(f23,axiom,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f313,plain,
! [X0] : multiply(inverse(inverse(identity)),X0) = X0,
inference(superposition,[],[f60,f189]) ).
fof(f189,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(superposition,[],[f60,f1]) ).
fof(f311,plain,
( ! [X0] : multiply(inverse(inverse(sk_c7)),multiply(sk_c8,X0)) = X0
| ~ spl0_1 ),
inference(forward_demodulation,[],[f310,f1]) ).
fof(f310,plain,
( ! [X0] : multiply(identity,X0) = multiply(inverse(inverse(sk_c7)),multiply(sk_c8,X0))
| ~ spl0_1 ),
inference(superposition,[],[f3,f300]) ).
fof(f309,plain,
( sk_c8 = multiply(inverse(inverse(inverse(sk_c7))),identity)
| ~ spl0_1 ),
inference(superposition,[],[f60,f300]) ).
fof(f300,plain,
( identity = multiply(inverse(inverse(sk_c7)),sk_c8)
| ~ spl0_1 ),
inference(superposition,[],[f60,f294]) ).
fof(f308,plain,
( ! [X0] : multiply(inverse(inverse(sk_c2)),multiply(sk_c1,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f307,f1]) ).
fof(f307,plain,
( ! [X0] : multiply(identity,X0) = multiply(inverse(inverse(sk_c2)),multiply(sk_c1,X0))
| ~ spl0_2 ),
inference(superposition,[],[f3,f297]) ).
fof(f297,plain,
( identity = multiply(inverse(inverse(sk_c2)),sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f60,f200]) ).
fof(f303,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(inverse(sk_c7),X0)
| ~ spl0_1 ),
inference(superposition,[],[f60,f292]) ).
fof(f292,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = X0
| ~ spl0_1 ),
inference(superposition,[],[f60,f40]) ).
fof(f294,plain,
( sk_c8 = multiply(inverse(sk_c7),identity)
| ~ spl0_1 ),
inference(superposition,[],[f60,f293]) ).
fof(f299,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(inverse(sk_c2),X0)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f298,f1]) ).
fof(f298,plain,
( ! [X0] : multiply(sk_c1,X0) = multiply(inverse(sk_c2),multiply(identity,X0))
| ~ spl0_2 ),
inference(superposition,[],[f3,f200]) ).
fof(f200,plain,
( sk_c1 = multiply(inverse(sk_c2),identity)
| ~ spl0_2 ),
inference(superposition,[],[f60,f46]) ).
fof(f296,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = X0
| ~ spl0_1 ),
inference(forward_demodulation,[],[f295,f1]) ).
fof(f295,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0))
| ~ spl0_1 ),
inference(superposition,[],[f3,f293]) ).
fof(f293,plain,
( identity = multiply(sk_c7,sk_c8)
| ~ spl0_1 ),
inference(superposition,[],[f2,f40]) ).
fof(f40,plain,
( inverse(sk_c8) = sk_c7
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f38,plain,
( spl0_1
<=> inverse(sk_c8) = sk_c7 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f22,axiom,
( sk_c8 = inverse(sk_c3)
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f27,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f4,axiom,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f16,axiom,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c2,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f25,axiom,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f26,axiom,
( sk_c8 = inverse(sk_c3)
| sk_c6 = multiply(sk_c5,sk_c8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f28,axiom,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f33,axiom,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f31,axiom,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f32,axiom,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f36,plain,
! [X3,X8,X6,X5] :
( sk_c8 != inverse(X8)
| sk_c8 != inverse(X5)
| sk_c8 != inverse(X6)
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) ),
inference(equality_resolution,[],[f35]) ).
fof(f35,plain,
! [X3,X8,X6,X7,X5] :
( sk_c8 != inverse(X8)
| sk_c8 != inverse(X5)
| sk_c8 != inverse(X6)
| inverse(sk_c8) != sk_c7
| sk_c7 != multiply(sk_c8,X7)
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3))
| multiply(X8,sk_c8) != X7 ),
inference(equality_resolution,[],[f34]) ).
fof(f34,axiom,
! [X3,X8,X6,X7,X4,X5] :
( sk_c8 != inverse(X8)
| sk_c8 != inverse(X5)
| sk_c8 != inverse(X6)
| inverse(sk_c8) != sk_c7
| inverse(X3) != X4
| sk_c7 != multiply(sk_c8,X7)
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(X4,sk_c7)
| sk_c8 != multiply(X3,X4)
| multiply(X8,sk_c8) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f193,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f60,f3]) ).
fof(f60,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f53,f1]) ).
fof(f53,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f3,f2]) ).
fof(f63,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c1,X0)) = X0
| ~ spl0_2 ),
inference(forward_demodulation,[],[f55,f1]) ).
fof(f55,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(sk_c1,X0))
| ~ spl0_2 ),
inference(superposition,[],[f3,f46]) ).
fof(f3,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
fof(f46,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_2 ),
inference(superposition,[],[f2,f44]) ).
fof(f10,axiom,
( sk_c2 = inverse(sk_c1)
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f2,axiom,
! [X0] : identity = multiply(inverse(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f12,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f11,axiom,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f3596,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f3595]) ).
fof(f3595,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f3594,f2125]) ).
fof(f3594,plain,
( identity = sk_c8
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f3583,f2]) ).
fof(f3583,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f60,f3553]) ).
fof(f3553,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f3461,f3543]) ).
fof(f3543,plain,
( sk_c8 = sk_c7
| ~ spl0_2
| spl0_9
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f3542,f2125]) ).
fof(f3542,plain,
( identity = sk_c8
| sk_c8 = sk_c7
| ~ spl0_2
| ~ spl0_10 ),
inference(forward_demodulation,[],[f3424,f3080]) ).
fof(f3424,plain,
( sk_c8 = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f3423,f718]) ).
fof(f3423,plain,
( sk_c7 = multiply(sk_c8,identity)
| multiply(sk_c1,sk_c2) = sk_c8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f7,f3141]) ).
fof(f3141,plain,
( identity = sk_c6
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f3139]) ).
fof(f3461,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9 ),
inference(forward_demodulation,[],[f3418,f2077]) ).
fof(f2077,plain,
( sk_c7 = sk_c4
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f2076,f395]) ).
fof(f2076,plain,
( sk_c4 = multiply(sk_c7,identity)
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f2066,f40]) ).
fof(f2066,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_4 ),
inference(superposition,[],[f190,f323]) ).
fof(f323,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f321,plain,
( spl0_4
<=> sk_c8 = inverse(sk_c4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f3591,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f3590]) ).
fof(f3590,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f3589,f2125]) ).
fof(f3589,plain,
( identity = sk_c8
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f3580,f715]) ).
fof(f3580,plain,
( sk_c8 = multiply(sk_c8,inverse(sk_c8))
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f1308,f3553]) ).
fof(f3587,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f3586]) ).
fof(f3586,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(subsumption_resolution,[],[f3585,f2125]) ).
fof(f3585,plain,
( identity = sk_c8
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f3578,f293]) ).
fof(f3578,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4
| spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f292,f3553]) ).
fof(f3412,plain,
( spl0_5
| spl0_6
| spl0_6
| spl0_7
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f2923,f2124,f38,f1960,f1957,f1957,f1954]) ).
fof(f1954,plain,
( spl0_5
<=> ! [X8] :
( identity != multiply(identity,X8)
| identity != inverse(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1957,plain,
( spl0_6
<=> ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1960,plain,
( spl0_7
<=> ! [X3] : identity != multiply(inverse(X3),identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f2923,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(inverse(X3),identity)
| identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6) )
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2922,f2575]) ).
fof(f2575,plain,
( identity = sk_c7
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2568,f1144]) ).
fof(f2568,plain,
( sk_c7 = inverse(identity)
| ~ spl0_1
| ~ spl0_9 ),
inference(superposition,[],[f40,f2126]) ).
fof(f2126,plain,
( identity = sk_c8
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f2124]) ).
fof(f2922,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2921,f2575]) ).
fof(f2921,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2920,f2575]) ).
fof(f2920,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(X6,sk_c7)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2733,f2575]) ).
fof(f2733,plain,
( ! [X3,X8,X6,X5] :
( sk_c7 != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(X6,sk_c7)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2038,f2126]) ).
fof(f3146,plain,
( spl0_10
| spl0_11
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f2940,f2124,f2120,f38,f3143,f3139]) ).
fof(f3143,plain,
( spl0_11
<=> identity = sk_c2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f2940,plain,
( identity = sk_c2
| identity = sk_c6
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2939,f2126]) ).
fof(f2939,plain,
( sk_c2 = sk_c8
| identity = sk_c6
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2938,f718]) ).
fof(f2938,plain,
( sk_c8 = multiply(sk_c2,identity)
| identity = sk_c6
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2937,f2575]) ).
fof(f2937,plain,
( identity = sk_c6
| sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2703,f2575]) ).
fof(f2703,plain,
( sk_c7 = sk_c6
| sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2702,f395]) ).
fof(f2702,plain,
( sk_c6 = multiply(sk_c7,identity)
| sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2701,f2145]) ).
fof(f2701,plain,
( sk_c6 = multiply(sk_c5,identity)
| sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_9 ),
inference(forward_demodulation,[],[f20,f2126]) ).
fof(f2912,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2911]) ).
fof(f2911,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2910,f1]) ).
fof(f2910,plain,
( identity != multiply(identity,identity)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2888,f2126]) ).
fof(f2888,plain,
( identity != multiply(sk_c8,identity)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f1961,f302]) ).
fof(f1961,plain,
( ! [X3] : identity != multiply(inverse(X3),identity)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f2909,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2908]) ).
fof(f2908,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2881,f2126]) ).
fof(f2881,plain,
( identity != sk_c8
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f1961,f294]) ).
fof(f2907,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2906]) ).
fof(f2906,plain,
( $false
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2905,f1]) ).
fof(f2905,plain,
( identity != multiply(identity,identity)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2879,f2126]) ).
fof(f2879,plain,
( identity != multiply(sk_c8,identity)
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f1961,f2122]) ).
fof(f2904,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2903]) ).
fof(f2903,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2902,f1]) ).
fof(f2902,plain,
( identity != multiply(identity,identity)
| ~ spl0_1
| spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2901,f2126]) ).
fof(f2901,plain,
( identity != multiply(sk_c8,identity)
| ~ spl0_1
| spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2878,f2404]) ).
fof(f2404,plain,
( sk_c8 = sk_c7
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2215,f718]) ).
fof(f2215,plain,
( sk_c7 = multiply(sk_c8,identity)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f2176,f2213]) ).
fof(f2213,plain,
( identity = sk_c6
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2212,f293]) ).
fof(f2212,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2211,f2145]) ).
fof(f2211,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| spl0_2 ),
inference(subsumption_resolution,[],[f14,f43]) ).
fof(f43,plain,
( sk_c2 != inverse(sk_c1)
| spl0_2 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f2176,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| spl0_2 ),
inference(subsumption_resolution,[],[f13,f43]) ).
fof(f2878,plain,
( identity != multiply(sk_c7,identity)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f1961,f40]) ).
fof(f2900,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2899]) ).
fof(f2899,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2898,f1]) ).
fof(f2898,plain,
( identity != multiply(identity,identity)
| ~ spl0_1
| spl0_2
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2877,f2126]) ).
fof(f2877,plain,
( identity != multiply(sk_c8,identity)
| ~ spl0_1
| spl0_2
| ~ spl0_7
| ~ spl0_8 ),
inference(superposition,[],[f1961,f2447]) ).
fof(f2447,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f737,f2404]) ).
fof(f2897,plain,
( ~ spl0_1
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f2896]) ).
fof(f2896,plain,
( $false
| ~ spl0_1
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f2875,f1]) ).
fof(f2875,plain,
( identity != multiply(identity,identity)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f1961,f1144]) ).
fof(f2895,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f2894]) ).
fof(f2894,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f2883]) ).
fof(f2883,plain,
( identity != identity
| ~ spl0_7 ),
inference(superposition,[],[f1961,f2]) ).
fof(f2893,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f2892]) ).
fof(f2892,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f2884]) ).
fof(f2884,plain,
( identity != identity
| ~ spl0_7 ),
inference(superposition,[],[f1961,f189]) ).
fof(f2891,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f2890]) ).
fof(f2890,plain,
( $false
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f2887]) ).
fof(f2887,plain,
( identity != identity
| ~ spl0_7 ),
inference(superposition,[],[f1961,f627]) ).
fof(f2865,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2864]) ).
fof(f2864,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2863,f1144]) ).
fof(f2863,plain,
( identity != inverse(identity)
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2862,f2126]) ).
fof(f2862,plain,
( identity != inverse(sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2861,f2404]) ).
fof(f2861,plain,
( identity != inverse(sk_c7)
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2860,f40]) ).
fof(f2860,plain,
( identity != inverse(inverse(sk_c8))
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2859,f2404]) ).
fof(f2859,plain,
( identity != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2858,f2126]) ).
fof(f2858,plain,
( identity != sk_c8
| identity != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_6 ),
inference(forward_demodulation,[],[f2822,f718]) ).
fof(f2822,plain,
( identity != multiply(sk_c8,identity)
| identity != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f1958,f302]) ).
fof(f1958,plain,
( ! [X6] :
( identity != multiply(X6,identity)
| identity != inverse(X6) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f1957]) ).
fof(f2857,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f2856]) ).
fof(f2856,plain,
( $false
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f2855,f740]) ).
fof(f2855,plain,
( identity != inverse(inverse(identity))
| ~ spl0_6 ),
inference(forward_demodulation,[],[f2826,f740]) ).
fof(f2826,plain,
( identity != inverse(inverse(inverse(inverse(identity))))
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f2821]) ).
fof(f2821,plain,
( identity != identity
| identity != inverse(inverse(inverse(inverse(identity))))
| ~ spl0_6 ),
inference(superposition,[],[f1958,f627]) ).
fof(f2848,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f2847]) ).
fof(f2847,plain,
( $false
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f2827,f740]) ).
fof(f2827,plain,
( identity != inverse(inverse(identity))
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f2818]) ).
fof(f2818,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_6 ),
inference(superposition,[],[f1958,f189]) ).
fof(f2846,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f2845]) ).
fof(f2845,plain,
( $false
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f2828,f740]) ).
fof(f2828,plain,
( identity != inverse(inverse(identity))
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f2817]) ).
fof(f2817,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_6 ),
inference(superposition,[],[f1958,f2]) ).
fof(f2844,plain,
( ~ spl0_1
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f2843]) ).
fof(f2843,plain,
( $false
| ~ spl0_1
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f2829,f1144]) ).
fof(f2829,plain,
( identity != inverse(identity)
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f2816]) ).
fof(f2816,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_6 ),
inference(superposition,[],[f1958,f1]) ).
fof(f2842,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2841]) ).
fof(f2841,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2840,f1144]) ).
fof(f2840,plain,
( identity != inverse(identity)
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2839,f2126]) ).
fof(f2839,plain,
( identity != inverse(sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2838,f2404]) ).
fof(f2838,plain,
( identity != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2815,f2575]) ).
fof(f2815,plain,
( identity != sk_c7
| identity != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f1958,f395]) ).
fof(f2837,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f2836]) ).
fof(f2836,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2835,f1144]) ).
fof(f2835,plain,
( identity != inverse(identity)
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2834,f2126]) ).
fof(f2834,plain,
( identity != inverse(sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2833,f2404]) ).
fof(f2833,plain,
( identity != inverse(sk_c7)
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2832,f40]) ).
fof(f2832,plain,
( identity != inverse(inverse(sk_c8))
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2831,f2404]) ).
fof(f2831,plain,
( identity != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(subsumption_resolution,[],[f2814,f2126]) ).
fof(f2814,plain,
( identity != sk_c8
| identity != inverse(inverse(sk_c7))
| ~ spl0_1
| ~ spl0_6 ),
inference(superposition,[],[f1958,f294]) ).
fof(f2805,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f2804]) ).
fof(f2804,plain,
( $false
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f2795,f740]) ).
fof(f2795,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f2792]) ).
fof(f2792,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_5 ),
inference(superposition,[],[f1955,f715]) ).
fof(f1955,plain,
( ! [X8] :
( identity != multiply(identity,X8)
| identity != inverse(X8) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f1954]) ).
fof(f2803,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f2802]) ).
fof(f2802,plain,
( $false
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f2801,f740]) ).
fof(f2801,plain,
( identity != inverse(inverse(identity))
| ~ spl0_5 ),
inference(forward_demodulation,[],[f2796,f1186]) ).
fof(f2796,plain,
( ! [X0] : identity != inverse(multiply(X0,inverse(multiply(identity,X0))))
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f2791]) ).
fof(f2791,plain,
( ! [X0] :
( identity != identity
| identity != inverse(multiply(X0,inverse(multiply(identity,X0)))) )
| ~ spl0_5 ),
inference(superposition,[],[f1955,f858]) ).
fof(f2799,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f2798]) ).
fof(f2798,plain,
( $false
| ~ spl0_1
| ~ spl0_5 ),
inference(subsumption_resolution,[],[f2797,f1144]) ).
fof(f2797,plain,
( identity != inverse(identity)
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f2789]) ).
fof(f2789,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_5 ),
inference(superposition,[],[f1955,f718]) ).
fof(f2754,plain,
( spl0_5
| spl0_6
| spl0_6
| spl0_7
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f2741,f2124,f2120,f42,f38,f1960,f1957,f1957,f1954]) ).
fof(f2741,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(inverse(X3),identity)
| identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6) )
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2740,f2126]) ).
fof(f2740,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(inverse(X3),sk_c8)
| identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6) )
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2739,f2404]) ).
fof(f2739,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2738,f2126]) ).
fof(f2738,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X5,sk_c8)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2737,f2404]) ).
fof(f2737,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2736,f2126]) ).
fof(f2736,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X6,sk_c8)
| identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2735,f2404]) ).
fof(f2735,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(X6,sk_c7)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2734,f2126]) ).
fof(f2734,plain,
( ! [X3,X8,X6,X5] :
( sk_c8 != multiply(identity,X8)
| identity != inverse(X8)
| identity != inverse(X5)
| identity != inverse(X6)
| identity != multiply(X6,sk_c7)
| identity != multiply(X5,sk_c7)
| identity != multiply(inverse(X3),sk_c7) )
| ~ spl0_1
| spl0_2
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f2733,f2404]) ).
fof(f2557,plain,
( spl0_2
| ~ spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f2556]) ).
fof(f2556,plain,
( $false
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(global_subsumption,[],[f319,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f4,f27,f22,f189,f313,f23,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532,f5,f322]) ).
fof(f322,plain,
( sk_c8 != inverse(sk_c4)
| spl0_4 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f2532,plain,
( sk_c8 = inverse(sk_c4)
| spl0_2 ),
inference(subsumption_resolution,[],[f11,f43]) ).
fof(f2183,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c6,X0))
| spl0_2 ),
inference(superposition,[],[f3,f2176]) ).
fof(f2179,plain,
( sk_c8 = multiply(sk_c7,inverse(sk_c6))
| spl0_2 ),
inference(superposition,[],[f1308,f2176]) ).
fof(f319,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f317,plain,
( spl0_3
<=> sk_c8 = inverse(sk_c3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f2555,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2554]) ).
fof(f2554,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2553,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f4,f27,f22,f189,f313,f23,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532,f5,f322]) ).
fof(f2553,plain,
( sk_c8 = sk_c3
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f400,f2404]) ).
fof(f400,plain,
( sk_c7 = sk_c3
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f395,f330]) ).
fof(f330,plain,
( sk_c3 = multiply(sk_c7,identity)
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f328,f40]) ).
fof(f328,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_3 ),
inference(superposition,[],[f60,f326]) ).
fof(f326,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_3 ),
inference(superposition,[],[f2,f319]) ).
fof(f2552,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2551]) ).
fof(f2551,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2235,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f4,f27,f22,f189,f313,f23,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532,f5,f322]) ).
fof(f2235,plain,
( sk_c8 = sk_c3
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2223,f353]) ).
fof(f353,plain,
( sk_c8 = multiply(sk_c8,identity)
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f343,f293]) ).
fof(f343,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f325,f334]) ).
fof(f334,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c3,X0)
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f333,f1]) ).
fof(f333,plain,
( ! [X0] : multiply(sk_c3,X0) = multiply(sk_c7,multiply(identity,X0))
| ~ spl0_1
| ~ spl0_3 ),
inference(superposition,[],[f3,f330]) ).
fof(f325,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c3,X0)) = X0
| ~ spl0_3 ),
inference(superposition,[],[f60,f319]) ).
fof(f2223,plain,
( sk_c3 = multiply(sk_c8,identity)
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f330,f2217]) ).
fof(f2217,plain,
( sk_c8 = sk_c7
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2215,f353]) ).
fof(f2549,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2548]) ).
fof(f2548,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2547,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f4,f27,f22,f189,f313,f23,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532,f5,f322]) ).
fof(f2547,plain,
( sk_c8 = sk_c3
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2546,f2404]) ).
fof(f2546,plain,
( sk_c7 = sk_c3
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f814,f40]) ).
fof(f814,plain,
( inverse(sk_c8) = sk_c3
| ~ spl0_3 ),
inference(superposition,[],[f740,f319]) ).
fof(f2545,plain,
( spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f2544]) ).
fof(f2544,plain,
( $false
| spl0_2
| spl0_4 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f4,f27,f22,f189,f313,f23,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532,f5,f322]) ).
fof(f2543,plain,
( spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f2542]) ).
fof(f2542,plain,
( $false
| spl0_2
| spl0_4 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f4,f27,f22,f189,f313,f23,f322,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532,f5]) ).
fof(f2541,plain,
( ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2540]) ).
fof(f2540,plain,
( $false
| ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2539,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f5,f4,f27,f22,f189,f313,f23,f322,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532]) ).
fof(f2539,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| multiply(sk_c1,sk_c2) = sk_c8
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f6,f2404]) ).
fof(f2538,plain,
( ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2537]) ).
fof(f2537,plain,
( $false
| ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2536,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f5,f4,f27,f22,f189,f313,f23,f322,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532]) ).
fof(f2536,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2535,f2404]) ).
fof(f2535,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| spl0_2 ),
inference(subsumption_resolution,[],[f12,f43]) ).
fof(f2534,plain,
( spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f2533]) ).
fof(f2533,plain,
( $false
| spl0_2
| spl0_4 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f5,f4,f27,f22,f189,f313,f23,f322,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692,f2532]) ).
fof(f2531,plain,
( ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2530]) ).
fof(f2530,plain,
( $false
| ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2529,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f5,f4,f27,f22,f189,f313,f23,f322,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692]) ).
fof(f2529,plain,
( sk_c8 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f17,f2404]) ).
fof(f2528,plain,
( ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2527]) ).
fof(f2527,plain,
( $false
| ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2526,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f5,f4,f27,f22,f189,f313,f23,f322,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692]) ).
fof(f2526,plain,
( sk_c8 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c4)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f29,f2404]) ).
fof(f2525,plain,
( ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2524]) ).
fof(f2524,plain,
( $false
| ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2523,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f5,f4,f27,f22,f189,f313,f23,f322,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692]) ).
fof(f2523,plain,
( sk_c8 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2522,f2404]) ).
fof(f2522,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c7)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f30,f2404]) ).
fof(f2521,plain,
( ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f2520]) ).
fof(f2520,plain,
( $false
| ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_8 ),
inference(global_subsumption,[],[f2519,f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f5,f4,f27,f22,f189,f313,f23,f322,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1986,f1396,f1240,f1232,f1221,f2002,f2009,f2010,f1000,f990,f1097,f2032,f962,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f43,f2176,f2179,f2183,f1983,f1975,f1837,f1440,f1255,f1160,f1159,f1146,f1145,f2043,f2040,f859,f852,f759,f758,f744,f743,f695,f692]) ).
fof(f2519,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c3)
| ~ spl0_1
| spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f24,f2404]) ).
fof(f2518,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8
| spl0_9 ),
inference(avatar_contradiction_clause,[],[f2517]) ).
fof(f2517,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8
| spl0_9 ),
inference(subsumption_resolution,[],[f2516,f2125]) ).
fof(f2516,plain,
( identity = sk_c8
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2505,f2]) ).
fof(f2505,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f60,f2471]) ).
fof(f2471,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2399,f2404]) ).
fof(f2399,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| ~ spl0_1
| spl0_2
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f2129,f43]) ).
fof(f2129,plain,
( sk_c8 = multiply(sk_c7,sk_c7)
| sk_c2 = inverse(sk_c1)
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f12,f2077]) ).
fof(f2513,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8
| spl0_9 ),
inference(avatar_contradiction_clause,[],[f2512]) ).
fof(f2512,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8
| spl0_9 ),
inference(subsumption_resolution,[],[f2511,f2125]) ).
fof(f2511,plain,
( identity = sk_c8
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2502,f715]) ).
fof(f2502,plain,
( sk_c8 = multiply(sk_c8,inverse(sk_c8))
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f1308,f2471]) ).
fof(f2509,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8
| spl0_9 ),
inference(avatar_contradiction_clause,[],[f2508]) ).
fof(f2508,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8
| spl0_9 ),
inference(subsumption_resolution,[],[f2507,f2125]) ).
fof(f2507,plain,
( identity = sk_c8
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2500,f293]) ).
fof(f2500,plain,
( sk_c8 = multiply(sk_c7,sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f292,f2471]) ).
fof(f2403,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| spl0_9 ),
inference(avatar_contradiction_clause,[],[f2402]) ).
fof(f2402,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| spl0_9 ),
inference(subsumption_resolution,[],[f2401,f2125]) ).
fof(f2401,plain,
( identity = sk_c8
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2400,f2219]) ).
fof(f2219,plain,
( identity = multiply(sk_c8,sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_8 ),
inference(superposition,[],[f293,f2217]) ).
fof(f2400,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_1
| spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8 ),
inference(forward_demodulation,[],[f2399,f2217]) ).
fof(f2131,plain,
( spl0_2
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f2130]) ).
fof(f2130,plain,
( $false
| spl0_2
| spl0_8 ),
inference(global_subsumption,[],[f11,f12,f1,f2,f10,f3,f60,f193,f36,f32,f31,f30,f6,f33,f29,f28,f26,f25,f24,f16,f5,f4,f27,f22,f189,f313,f23,f190,f637,f627,f693,f707,f199,f723,f724,f728,f729,f718,f790,f755,f808,f740,f825,f826,f715,f892,f872,f719,f924,f937,f858,f969,f1005,f1153,f1188,f1191,f1186,f1200,f1219,f1237,f1385,f1250,f1251,f1253,f1254,f1308,f1395,f1414,f1435,f1436,f1437,f1438,f1429,f1553,f1556,f1557,f1558,f1559,f1190,f1619,f1630,f1645,f1646,f1647,f1648,f1650,f1651,f1314,f1762,f1780,f1781,f1798,f1802,f1804,f1691,f1907,f1913,f1917,f1919,f1963,f1837,f1975,f1754,f1635,f1625,f1978,f1980,f1981,f1602,f1561,f1555,f1983,f1986,f1396,f1440,f1240,f1232,f1221,f2002,f2009,f2010,f1255,f1160,f1159,f1146,f1145,f1000,f990,f1097,f2032,f962,f859,f852,f2040,f759,f758,f2043,f744,f743,f695,f692,f20,f19,f18,f21,f17,f9,f7,f8,f14,f13,f15,f2121,f43]) ).
fof(f2121,plain,
( sk_c8 != inverse(sk_c5)
| spl0_8 ),
inference(avatar_component_clause,[],[f2120]) ).
fof(f2127,plain,
( spl0_8
| spl0_9
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f2062,f42,f2124,f2120]) ).
fof(f1962,plain,
( spl0_5
| spl0_6
| spl0_6
| spl0_7
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[],[f958,f321,f42,f38,f1960,f1957,f1957,f1954]) ).
fof(f958,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(inverse(X3),identity)
| identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(subsumption_resolution,[],[f844,f715]) ).
fof(f844,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X3,inverse(X3))
| identity != multiply(inverse(X3),identity)
| identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f843,f417]) ).
fof(f417,plain,
( identity = sk_c8
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f416,f360]) ).
fof(f416,plain,
( multiply(sk_c1,sk_c2) = sk_c8
| spl0_4 ),
inference(subsumption_resolution,[],[f5,f322]) ).
fof(f843,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(inverse(X3),identity)
| identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f842,f417]) ).
fof(f842,plain,
( ! [X3,X8,X6,X5] :
( sk_c8 != multiply(inverse(X3),identity)
| identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f841,f436]) ).
fof(f436,plain,
( identity = sk_c7
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(superposition,[],[f420,f395]) ).
fof(f420,plain,
( identity = multiply(sk_c7,identity)
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(superposition,[],[f293,f417]) ).
fof(f841,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f840,f417]) ).
fof(f840,plain,
( ! [X3,X8,X6,X5] :
( sk_c8 != multiply(X5,identity)
| identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f839,f436]) ).
fof(f839,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f838,f417]) ).
fof(f838,plain,
( ! [X3,X8,X6,X5] :
( sk_c8 != multiply(X6,identity)
| identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f837,f436]) ).
fof(f837,plain,
( ! [X3,X8,X6,X5] :
( identity != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f836,f436]) ).
fof(f836,plain,
( ! [X3,X8,X6,X5] :
( sk_c7 != multiply(identity,X8)
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f835,f718]) ).
fof(f835,plain,
( ! [X3,X8,X6,X5] :
( sk_c7 != multiply(identity,multiply(X8,identity))
| identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f834,f417]) ).
fof(f834,plain,
( ! [X3,X8,X6,X5] :
( identity != inverse(X6)
| identity != inverse(X5)
| identity != inverse(X8)
| sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f833,f417]) ).
fof(f833,plain,
( ! [X3,X8,X6,X5] :
( identity != inverse(X5)
| identity != inverse(X8)
| sk_c8 != inverse(X6)
| sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f832,f417]) ).
fof(f832,plain,
( ! [X3,X8,X6,X5] :
( identity != inverse(X8)
| sk_c8 != inverse(X5)
| sk_c8 != inverse(X6)
| sk_c7 != multiply(sk_c8,multiply(X8,sk_c8))
| sk_c8 != multiply(X6,sk_c7)
| sk_c8 != multiply(X5,sk_c7)
| sk_c8 != multiply(inverse(X3),sk_c7)
| sk_c8 != multiply(X3,inverse(X3)) )
| ~ spl0_1
| ~ spl0_2
| spl0_4 ),
inference(forward_demodulation,[],[f831,f417]) ).
fof(f324,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f23,f321,f317]) ).
fof(f286,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f285]) ).
fof(f285,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f284,f250]) ).
fof(f250,plain,
( identity = sk_c2
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f238,f234]) ).
fof(f234,plain,
( identity = sk_c7
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f233,f2]) ).
fof(f233,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c2)
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f207,f85]) ).
fof(f85,plain,
( sk_c2 = sk_c8
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f84,f65]) ).
fof(f65,plain,
( sk_c2 = multiply(sk_c2,sk_c8)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f63,f49]) ).
fof(f49,plain,
( multiply(sk_c1,sk_c2) = sk_c8
| spl0_1 ),
inference(subsumption_resolution,[],[f4,f39]) ).
fof(f39,plain,
( inverse(sk_c8) != sk_c7
| spl0_1 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f84,plain,
( sk_c8 = multiply(sk_c2,sk_c8)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f50,f80]) ).
fof(f80,plain,
( sk_c8 = sk_c7
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f79,f49]) ).
fof(f79,plain,
( multiply(sk_c1,sk_c2) = sk_c7
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f75,f69]) ).
fof(f69,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| spl0_1 ),
inference(superposition,[],[f64,f51]) ).
fof(f51,plain,
( sk_c8 = multiply(sk_c3,sk_c7)
| spl0_1 ),
inference(subsumption_resolution,[],[f28,f39]) ).
fof(f64,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c3,X0)) = X0
| spl0_1 ),
inference(forward_demodulation,[],[f59,f1]) ).
fof(f59,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c3,X0))
| spl0_1 ),
inference(superposition,[],[f3,f48]) ).
fof(f48,plain,
( identity = multiply(sk_c8,sk_c3)
| spl0_1 ),
inference(superposition,[],[f2,f47]) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c3)
| spl0_1 ),
inference(subsumption_resolution,[],[f22,f39]) ).
fof(f75,plain,
( multiply(sk_c1,sk_c2) = multiply(sk_c8,sk_c8)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f56,f65]) ).
fof(f56,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c8,X0)
| spl0_1 ),
inference(superposition,[],[f3,f49]) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| spl0_1 ),
inference(subsumption_resolution,[],[f16,f39]) ).
fof(f207,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c8)
| spl0_1 ),
inference(superposition,[],[f60,f50]) ).
fof(f238,plain,
( sk_c2 = sk_c7
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f237,f88]) ).
fof(f88,plain,
( sk_c2 = multiply(sk_c2,sk_c2)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f65,f85]) ).
fof(f237,plain,
( sk_c7 = multiply(sk_c2,sk_c2)
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f236,f85]) ).
fof(f236,plain,
( sk_c7 = multiply(sk_c8,sk_c2)
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f235,f47]) ).
fof(f235,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c2)
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f208,f85]) ).
fof(f208,plain,
( sk_c7 = multiply(inverse(sk_c3),sk_c8)
| spl0_1 ),
inference(superposition,[],[f60,f51]) ).
fof(f284,plain,
( identity != sk_c2
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f283,f234]) ).
fof(f283,plain,
( sk_c2 != sk_c7
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f277,f140]) ).
fof(f140,plain,
( sk_c2 = inverse(identity)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f44,f126]) ).
fof(f126,plain,
( identity = sk_c1
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f118,f46]) ).
fof(f118,plain,
( ! [X0] : multiply(sk_c2,X0) = X0
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f115,f1]) ).
fof(f115,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(identity,X0))
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f3,f111]) ).
fof(f111,plain,
( identity = multiply(sk_c2,identity)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f63,f105]) ).
fof(f105,plain,
( identity = multiply(sk_c1,identity)
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f103,f48]) ).
fof(f103,plain,
( multiply(sk_c8,sk_c3) = multiply(sk_c1,identity)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f56,f89]) ).
fof(f89,plain,
( identity = multiply(sk_c2,sk_c3)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f48,f85]) ).
fof(f277,plain,
( sk_c7 != inverse(identity)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f39,f248]) ).
fof(f248,plain,
( identity = sk_c8
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f247,f1]) ).
fof(f247,plain,
( sk_c8 = multiply(identity,identity)
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f245,f129]) ).
fof(f129,plain,
( identity = sk_c3
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f118,f89]) ).
fof(f245,plain,
( sk_c8 = multiply(sk_c3,identity)
| spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f51,f234]) ).
fof(f45,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f10,f42,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP212-1 : TPTP v8.1.2. Released v2.5.0.
% 0.02/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.30 % Computer : n032.cluster.edu
% 0.08/0.30 % Model : x86_64 x86_64
% 0.08/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30 % Memory : 8042.1875MB
% 0.08/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30 % CPULimit : 300
% 0.08/0.30 % WCLimit : 300
% 0.08/0.30 % DateTime : Tue Apr 30 04:35:21 EDT 2024
% 0.08/0.30 % CPUTime :
% 0.08/0.30 % (4645)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.32 % (4646)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.32 % (4650)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)
% 0.13/0.32 % (4648)WARNING: value z3 for option sas not known
% 0.13/0.32 % (4652)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)
% 0.13/0.32 % (4648)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)
% 0.13/0.32 % (4651)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)
% 0.13/0.32 TRYING [1]
% 0.13/0.32 % (4647)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.32 % (4649)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.32 TRYING [2]
% 0.13/0.32 TRYING [1]
% 0.13/0.32 TRYING [2]
% 0.13/0.32 TRYING [3]
% 0.13/0.33 TRYING [3]
% 0.13/0.33 TRYING [4]
% 0.13/0.34 TRYING [4]
% 0.13/0.35 TRYING [5]
% 0.13/0.39 % (4648)First to succeed.
% 0.13/0.39 TRYING [6]
% 0.13/0.40 % (4648)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.41 % (4648)------------------------------
% 0.13/0.41 % (4648)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.41 % (4648)Termination reason: Refutation
% 0.13/0.41
% 0.13/0.41 % (4648)Memory used [KB]: 1937
% 0.13/0.41 % (4648)Time elapsed: 0.079 s
% 0.13/0.41 % (4648)Instructions burned: 173 (million)
% 0.13/0.41 % (4648)------------------------------
% 0.13/0.41 % (4648)------------------------------
% 0.13/0.41 % (4645)Success in time 0.098 s
%------------------------------------------------------------------------------