TSTP Solution File: SWC213+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC213+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.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 May 21 05:03:21 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 175
% Syntax : Number of formulae : 998 ( 73 unt; 0 def)
% Number of atoms : 4370 (1154 equ)
% Maximal formula atoms : 48 ( 4 avg)
% Number of connectives : 5297 (1925 ~;2149 |; 840 &)
% ( 85 <=>; 298 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 9 prp; 0-2 aty)
% Number of functors : 58 ( 58 usr; 9 con; 0-2 aty)
% Number of variables : 2089 (1726 !; 363 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1126,plain,
$false,
inference(avatar_sat_refutation,[],[f659,f792,f908,f918,f1088,f1121,f1123,f1125]) ).
fof(f1125,plain,
( ~ spl71_1
| ~ spl71_2 ),
inference(avatar_contradiction_clause,[],[f1124]) ).
fof(f1124,plain,
( $false
| ~ spl71_1
| ~ spl71_2 ),
inference(global_subsumption,[],[f391,f389,f388,f386,f413,f415,f416,f425,f641,f426,f427,f428,f429,f430,f433,f431,f639,f435,f434,f443,f451,f455,f454,f453,f466,f469,f617,f485,f638,f496,f620,f508,f621,f520,f622,f532,f623,f543,f624,f553,f625,f626,f627,f628,f567,f629,f570,f569,f568,f573,f574,f575,f576,f577,f578,f631,f582,f581,f632,f586,f585,f584,f633,f589,f588,f636,f592,f591,f594,f596,f595,f597,f598,f599,f600,f601,f602,f603,f604,f605,f377,f378,f379,f380,f384,f385,f387,f392,f393,f394,f395,f396,f397,f398,f399,f400,f606,f607,f381,f382,f648,f383,f390,f608,f613,f615,f643,f644,f645,f487,f499,f511,f523,f534,f545,f555,f650,f401,f402,f403,f404,f456,f457,f458,f459,f460,f461,f480,f481,f482,f483,f484,f491,f492,f493,f494,f495,f503,f504,f505,f506,f507,f515,f516,f517,f518,f519,f527,f528,f529,f530,f531,f538,f539,f540,f541,f542,f549,f550,f551,f552,f637,f642,f646,f662,f405,f406,f407,f408,f409,f410,f411,f477,f488,f500,f512,f524,f525,f535,f536,f546,f663,f664,f444,f665,f666,f667,f668,f669,f670,f671,f452,f462,f703,f704,f677,f678,f463,f732,f733,f681,f682,f706,f707,f710,f711,f474,f486,f497,f498,f509,f510,f521,f522,f533,f544,f554,f440,f448,f464,f736,f737,f465,f467,f468,f738,f739,f470,f472,f740,f741,f556,f558,f560,f562,f757,f758,f572,f759,f760,f563,f564,f640,f683,f684,f685,f686,f687,f688,f689,f690,f691,f692,f412,f693,f694,f695,f772,f696,f773,f697,f774,f698,f775,f699,f776,f700,f777,f701,f702,f712,f414,f713,f714,f715,f716,f717,f718,f719,f720,f721,f722,f723,f418,f724,f793,f725,f794,f726,f795,f727,f796,f728,f797,f729,f798,f730,f731,f419,f420,f801,f421,f422,f424,f437,f438,f441,f445,f446,f449,f813,f814,f815,f471,f848,f817,f819,f826,f827,f828,f829,f830,f831,f832,f833,f834,f835,f836,f837,f838,f839,f840,f841,f842,f843,f844,f845,f846,f847,f473,f888,f857,f859,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f880,f881,f882,f883,f884,f885,f886,f887,f824,f475,f825,f565,f924,f925,f926,f927,f956,f957,f934,f935,f936,f937,f938,f939,f940,f941,f942,f943,f944,f945,f946,f947,f948,f949,f950,f951,f952,f953,f954,f955,f928,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f969,f970,f971,f972,f973,f974,f975,f976,f977,f566,f980,f981,f982,f983,f984,f985,f1012,f1013,f988,f989,f990,f991,f992,f993,f994,f995,f996,f997,f998,f999,f1000,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f929,f1014,f1015,f1016,f1017,f1018,f1019,f1020,f1021,f1022,f1023,f1024,f1025,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f932,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1048,f1049,f1050,f1051,f1052,f1053,f1054,f1055,f933,f1058,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1072,f1073,f1074,f1075,f1076,f1077,f580,f1090,f861,f1092,f821,f1094,f1095,f1096,f860,f1097,f1098,f1099,f820,f1100,f654,f1102,f657,f1105,f1113,f1111,f1112,f1101,f1115,f1118,f1119]) ).
fof(f1119,plain,
( nil = tl(cons(sK70,nil))
| ~ spl71_1 ),
inference(superposition,[],[f1033,f1101]) ).
fof(f1118,plain,
( nil = tl(cons(sK69,nil))
| ~ spl71_1 ),
inference(superposition,[],[f1032,f1101]) ).
fof(f1115,plain,
( neq(nil,nil)
| ~ spl71_1 ),
inference(superposition,[],[f383,f1101]) ).
fof(f1101,plain,
( nil = sK19
| ~ spl71_1 ),
inference(superposition,[],[f654,f381]) ).
fof(f1112,plain,
( nil = tl(cons(sK70,nil))
| ~ spl71_2 ),
inference(superposition,[],[f977,f657]) ).
fof(f1111,plain,
( nil = tl(cons(sK69,nil))
| ~ spl71_2 ),
inference(superposition,[],[f976,f657]) ).
fof(f1113,plain,
( sK19 = app(sK22,sK23)
| ~ spl71_2 ),
inference(forward_demodulation,[],[f1107,f681]) ).
fof(f1107,plain,
( sK19 = app(app(sK22,nil),sK23)
| ~ spl71_2 ),
inference(superposition,[],[f662,f657]) ).
fof(f1105,plain,
( ~ neq(nil,nil)
| ~ spl71_2 ),
inference(superposition,[],[f390,f657]) ).
fof(f657,plain,
( nil = sK18
| ~ spl71_2 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f656,plain,
( spl71_2
<=> nil = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_2])]) ).
fof(f1102,plain,
( nil = sK19
| ~ spl71_1 ),
inference(superposition,[],[f381,f654]) ).
fof(f654,plain,
( nil = sK21
| ~ spl71_1 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f652,plain,
( spl71_1
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_1])]) ).
fof(f1100,plain,
nil = sK18,
inference(global_subsumption,[],[f391,f389,f388,f386,f413,f415,f416,f425,f641,f426,f427,f428,f429,f430,f433,f431,f639,f435,f434,f443,f451,f455,f454,f453,f466,f469,f617,f485,f638,f496,f620,f508,f621,f520,f622,f532,f623,f543,f624,f553,f625,f626,f627,f628,f567,f629,f570,f569,f568,f573,f574,f575,f576,f577,f578,f631,f582,f581,f632,f586,f585,f584,f633,f589,f588,f636,f592,f591,f594,f596,f595,f597,f598,f599,f600,f601,f602,f603,f604,f605,f377,f378,f379,f380,f384,f385,f387,f392,f393,f394,f395,f396,f397,f398,f399,f400,f606,f607,f381,f382,f648,f383,f390,f608,f613,f615,f643,f644,f645,f487,f499,f511,f523,f534,f545,f555,f650,f401,f402,f403,f404,f456,f457,f458,f459,f460,f461,f480,f481,f482,f483,f484,f491,f492,f493,f494,f495,f503,f504,f505,f506,f507,f515,f516,f517,f518,f519,f527,f528,f529,f530,f531,f538,f539,f540,f541,f542,f549,f550,f551,f552,f637,f642,f646,f662,f405,f406,f407,f408,f409,f410,f411,f477,f488,f500,f512,f524,f525,f535,f536,f546,f663,f664,f444,f665,f666,f667,f668,f669,f670,f671,f452,f462,f703,f704,f677,f678,f463,f732,f733,f681,f682,f706,f707,f710,f711,f474,f486,f497,f498,f509,f510,f521,f522,f533,f544,f554,f440,f448,f464,f736,f737,f465,f467,f468,f738,f739,f470,f472,f740,f741,f556,f558,f560,f562,f757,f758,f572,f759,f760,f563,f564,f640,f683,f684,f685,f686,f687,f688,f689,f690,f691,f692,f412,f693,f694,f695,f772,f696,f773,f697,f774,f698,f775,f699,f776,f700,f777,f701,f702,f712,f414,f713,f714,f715,f716,f717,f718,f719,f720,f721,f722,f723,f418,f724,f793,f725,f794,f726,f795,f727,f796,f728,f797,f729,f798,f730,f731,f419,f420,f801,f421,f422,f424,f437,f438,f441,f445,f446,f449,f813,f814,f815,f471,f848,f817,f819,f826,f827,f828,f829,f830,f831,f832,f833,f834,f835,f836,f837,f838,f839,f840,f841,f842,f843,f844,f845,f846,f847,f473,f888,f857,f859,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f880,f881,f882,f883,f884,f885,f886,f887,f824,f475,f825,f565,f924,f925,f926,f927,f956,f957,f934,f935,f936,f937,f938,f939,f940,f941,f942,f943,f944,f945,f946,f947,f948,f949,f950,f951,f952,f953,f954,f955,f928,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f969,f970,f971,f972,f973,f974,f975,f976,f977,f566,f980,f981,f982,f983,f984,f985,f1012,f1013,f988,f989,f990,f991,f992,f993,f994,f995,f996,f997,f998,f999,f1000,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f929,f1014,f1015,f1016,f1017,f1018,f1019,f1020,f1021,f1022,f1023,f1024,f1025,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f932,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1048,f1049,f1050,f1051,f1052,f1053,f1054,f1055,f933,f1058,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1072,f1073,f1074,f1075,f1076,f1077,f580,f1090,f861,f1092,f821,f1094,f1095,f1096,f860,f1097,f1098,f1099,f820]) ).
fof(f820,plain,
( nil = sK18
| hd(sK18) = sK26(sK18) ),
inference(resolution,[],[f471,f377]) ).
fof(f1099,plain,
nil = sK18,
inference(global_subsumption,[],[f391,f389,f388,f386,f413,f415,f416,f425,f641,f426,f427,f428,f429,f430,f433,f431,f639,f435,f434,f443,f451,f455,f454,f453,f466,f469,f617,f485,f638,f496,f620,f508,f621,f520,f622,f532,f623,f543,f624,f553,f625,f626,f627,f628,f567,f629,f570,f569,f568,f573,f574,f575,f576,f577,f578,f631,f582,f581,f632,f586,f585,f584,f633,f589,f588,f636,f592,f591,f594,f596,f595,f597,f598,f599,f600,f601,f602,f603,f604,f605,f377,f378,f379,f380,f384,f385,f387,f392,f393,f394,f395,f396,f397,f398,f399,f400,f606,f607,f381,f382,f648,f383,f390,f608,f613,f615,f643,f644,f645,f487,f499,f511,f523,f534,f545,f555,f650,f401,f402,f403,f404,f456,f457,f458,f459,f460,f461,f480,f481,f482,f483,f484,f491,f492,f493,f494,f495,f503,f504,f505,f506,f507,f515,f516,f517,f518,f519,f527,f528,f529,f530,f531,f538,f539,f540,f541,f542,f549,f550,f551,f552,f637,f642,f646,f662,f405,f406,f407,f408,f409,f410,f411,f477,f488,f500,f512,f524,f525,f535,f536,f546,f663,f664,f444,f665,f666,f667,f668,f669,f670,f671,f452,f462,f703,f704,f677,f678,f463,f732,f733,f681,f682,f706,f707,f710,f711,f474,f486,f497,f498,f509,f510,f521,f522,f533,f544,f554,f440,f448,f464,f736,f737,f465,f467,f468,f738,f739,f470,f472,f740,f741,f556,f558,f560,f562,f757,f758,f572,f759,f760,f563,f564,f640,f683,f684,f685,f686,f687,f688,f689,f690,f691,f692,f412,f693,f694,f695,f772,f696,f773,f697,f774,f698,f775,f699,f776,f700,f777,f701,f702,f712,f414,f713,f714,f715,f716,f717,f718,f719,f720,f721,f722,f723,f418,f724,f793,f725,f794,f726,f795,f727,f796,f728,f797,f729,f798,f730,f731,f419,f420,f801,f421,f422,f424,f437,f438,f441,f445,f446,f449,f813,f814,f815,f471,f848,f817,f819,f826,f827,f828,f829,f830,f831,f832,f833,f834,f835,f836,f837,f838,f839,f840,f841,f842,f843,f844,f845,f846,f847,f473,f888,f857,f859,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f880,f881,f882,f883,f884,f885,f886,f887,f824,f475,f825,f565,f924,f925,f926,f927,f956,f957,f934,f935,f936,f937,f938,f939,f940,f941,f942,f943,f944,f945,f946,f947,f948,f949,f950,f951,f952,f953,f954,f955,f928,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f969,f970,f971,f972,f973,f974,f975,f976,f977,f566,f980,f981,f982,f983,f984,f985,f1012,f1013,f988,f989,f990,f991,f992,f993,f994,f995,f996,f997,f998,f999,f1000,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f929,f1014,f1015,f1016,f1017,f1018,f1019,f1020,f1021,f1022,f1023,f1024,f1025,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f932,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1048,f1049,f1050,f1051,f1052,f1053,f1054,f1055,f933,f1058,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1072,f1073,f1074,f1075,f1076,f1077,f580,f1090,f861,f1092,f821,f1094,f1095,f1096,f860,f1097,f1098]) ).
fof(f1098,plain,
( hd(sK18) = sK26(sK18)
| nil = sK18 ),
inference(forward_demodulation,[],[f851,f382]) ).
fof(f851,plain,
( nil = sK18
| hd(sK20) = sK26(sK20) ),
inference(forward_demodulation,[],[f822,f382]) ).
fof(f822,plain,
( nil = sK20
| hd(sK20) = sK26(sK20) ),
inference(resolution,[],[f471,f379]) ).
fof(f1097,plain,
nil = sK18,
inference(global_subsumption,[],[f391,f389,f388,f386,f413,f415,f416,f425,f641,f426,f427,f428,f429,f430,f433,f431,f639,f435,f434,f443,f451,f455,f454,f453,f466,f469,f617,f485,f638,f496,f620,f508,f621,f520,f622,f532,f623,f543,f624,f553,f625,f626,f627,f628,f567,f629,f570,f569,f568,f573,f574,f575,f576,f577,f578,f631,f582,f581,f632,f586,f585,f584,f633,f589,f588,f636,f592,f591,f594,f596,f595,f597,f598,f599,f600,f601,f602,f603,f604,f605,f377,f378,f379,f380,f384,f385,f387,f392,f393,f394,f395,f396,f397,f398,f399,f400,f606,f607,f381,f382,f648,f383,f390,f608,f613,f615,f643,f644,f645,f487,f499,f511,f523,f534,f545,f555,f650,f401,f402,f403,f404,f456,f457,f458,f459,f460,f461,f480,f481,f482,f483,f484,f491,f492,f493,f494,f495,f503,f504,f505,f506,f507,f515,f516,f517,f518,f519,f527,f528,f529,f530,f531,f538,f539,f540,f541,f542,f549,f550,f551,f552,f637,f642,f646,f662,f405,f406,f407,f408,f409,f410,f411,f477,f488,f500,f512,f524,f525,f535,f536,f546,f663,f664,f444,f665,f666,f667,f668,f669,f670,f671,f452,f462,f703,f704,f677,f678,f463,f732,f733,f681,f682,f706,f707,f710,f711,f474,f486,f497,f498,f509,f510,f521,f522,f533,f544,f554,f440,f448,f464,f736,f737,f465,f467,f468,f738,f739,f470,f472,f740,f741,f556,f558,f560,f562,f757,f758,f572,f759,f760,f563,f564,f640,f683,f684,f685,f686,f687,f688,f689,f690,f691,f692,f412,f693,f694,f695,f772,f696,f773,f697,f774,f698,f775,f699,f776,f700,f777,f701,f702,f712,f414,f713,f714,f715,f716,f717,f718,f719,f720,f721,f722,f723,f418,f724,f793,f725,f794,f726,f795,f727,f796,f728,f797,f729,f798,f730,f731,f419,f420,f801,f421,f422,f424,f437,f438,f441,f445,f446,f449,f813,f814,f815,f471,f848,f817,f819,f826,f827,f828,f829,f830,f831,f832,f833,f834,f835,f836,f837,f838,f839,f840,f841,f842,f843,f844,f845,f846,f847,f473,f888,f857,f859,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f880,f881,f882,f883,f884,f885,f886,f887,f824,f475,f825,f565,f924,f925,f926,f927,f956,f957,f934,f935,f936,f937,f938,f939,f940,f941,f942,f943,f944,f945,f946,f947,f948,f949,f950,f951,f952,f953,f954,f955,f928,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f969,f970,f971,f972,f973,f974,f975,f976,f977,f566,f980,f981,f982,f983,f984,f985,f1012,f1013,f988,f989,f990,f991,f992,f993,f994,f995,f996,f997,f998,f999,f1000,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f929,f1014,f1015,f1016,f1017,f1018,f1019,f1020,f1021,f1022,f1023,f1024,f1025,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f932,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1048,f1049,f1050,f1051,f1052,f1053,f1054,f1055,f933,f1058,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1072,f1073,f1074,f1075,f1076,f1077,f580,f1090,f861,f1092,f821,f1094,f1095,f1096,f860]) ).
fof(f860,plain,
( nil = sK18
| tl(sK18) = sK27(sK18) ),
inference(resolution,[],[f473,f377]) ).
fof(f1096,plain,
nil = sK18,
inference(global_subsumption,[],[f391,f389,f388,f386,f413,f415,f416,f425,f641,f426,f427,f428,f429,f430,f433,f431,f639,f435,f434,f443,f451,f455,f454,f453,f466,f469,f617,f485,f638,f496,f620,f508,f621,f520,f622,f532,f623,f543,f624,f553,f625,f626,f627,f628,f567,f629,f570,f569,f568,f573,f574,f575,f576,f577,f578,f631,f582,f581,f632,f586,f585,f584,f633,f589,f588,f636,f592,f591,f594,f596,f595,f597,f598,f599,f600,f601,f602,f603,f604,f605,f377,f378,f379,f380,f384,f385,f387,f392,f393,f394,f395,f396,f397,f398,f399,f400,f606,f607,f381,f382,f648,f383,f390,f608,f613,f615,f643,f644,f645,f487,f499,f511,f523,f534,f545,f555,f650,f401,f402,f403,f404,f456,f457,f458,f459,f460,f461,f480,f481,f482,f483,f484,f491,f492,f493,f494,f495,f503,f504,f505,f506,f507,f515,f516,f517,f518,f519,f527,f528,f529,f530,f531,f538,f539,f540,f541,f542,f549,f550,f551,f552,f637,f642,f646,f662,f405,f406,f407,f408,f409,f410,f411,f477,f488,f500,f512,f524,f525,f535,f536,f546,f663,f664,f444,f665,f666,f667,f668,f669,f670,f671,f452,f462,f703,f704,f677,f678,f463,f732,f733,f681,f682,f706,f707,f710,f711,f474,f486,f497,f498,f509,f510,f521,f522,f533,f544,f554,f440,f448,f464,f736,f737,f465,f467,f468,f738,f739,f470,f472,f740,f741,f556,f558,f560,f562,f757,f758,f572,f759,f760,f563,f564,f640,f683,f684,f685,f686,f687,f688,f689,f690,f691,f692,f412,f693,f694,f695,f772,f696,f773,f697,f774,f698,f775,f699,f776,f700,f777,f701,f702,f712,f414,f713,f714,f715,f716,f717,f718,f719,f720,f721,f722,f723,f418,f724,f793,f725,f794,f726,f795,f727,f796,f728,f797,f729,f798,f730,f731,f419,f420,f801,f421,f422,f424,f437,f438,f441,f445,f446,f449,f813,f814,f815,f471,f848,f817,f819,f826,f827,f828,f829,f830,f831,f832,f833,f834,f835,f836,f837,f838,f839,f840,f841,f842,f843,f844,f845,f846,f847,f473,f888,f857,f859,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f880,f881,f882,f883,f884,f885,f886,f887,f824,f475,f825,f565,f924,f925,f926,f927,f956,f957,f934,f935,f936,f937,f938,f939,f940,f941,f942,f943,f944,f945,f946,f947,f948,f949,f950,f951,f952,f953,f954,f955,f928,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f969,f970,f971,f972,f973,f974,f975,f976,f977,f566,f980,f981,f982,f983,f984,f985,f1012,f1013,f988,f989,f990,f991,f992,f993,f994,f995,f996,f997,f998,f999,f1000,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f929,f1014,f1015,f1016,f1017,f1018,f1019,f1020,f1021,f1022,f1023,f1024,f1025,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f932,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1048,f1049,f1050,f1051,f1052,f1053,f1054,f1055,f933,f1058,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1072,f1073,f1074,f1075,f1076,f1077,f580,f1090,f861,f1092,f821,f1094,f1095]) ).
fof(f1095,plain,
( tl(sK18) = sK27(sK18)
| nil = sK18 ),
inference(forward_demodulation,[],[f891,f382]) ).
fof(f891,plain,
( nil = sK18
| tl(sK20) = sK27(sK20) ),
inference(forward_demodulation,[],[f862,f382]) ).
fof(f862,plain,
( nil = sK20
| tl(sK20) = sK27(sK20) ),
inference(resolution,[],[f473,f379]) ).
fof(f1094,plain,
nil = sK18,
inference(subsumption_resolution,[],[f1093,f377]) ).
fof(f1093,plain,
( nil = sK18
| ~ ssList(sK18) ),
inference(subsumption_resolution,[],[f1080,f400]) ).
fof(f1080,plain,
( nil = sK18
| ~ ssList(nil)
| ~ ssList(sK18) ),
inference(resolution,[],[f580,f390]) ).
fof(f821,plain,
( nil = sK19
| hd(sK19) = sK26(sK19) ),
inference(resolution,[],[f471,f378]) ).
fof(f1092,plain,
( hd(sK19) = sK26(sK19)
| nil = sK19 ),
inference(forward_demodulation,[],[f1091,f381]) ).
fof(f1091,plain,
( nil = sK19
| hd(sK21) = sK26(sK21) ),
inference(forward_demodulation,[],[f823,f381]) ).
fof(f823,plain,
( nil = sK21
| hd(sK21) = sK26(sK21) ),
inference(resolution,[],[f471,f380]) ).
fof(f861,plain,
( nil = sK19
| tl(sK19) = sK27(sK19) ),
inference(resolution,[],[f473,f378]) ).
fof(f1090,plain,
( tl(sK19) = sK27(sK19)
| nil = sK19 ),
inference(forward_demodulation,[],[f1089,f381]) ).
fof(f1089,plain,
( nil = sK19
| tl(sK21) = sK27(sK21) ),
inference(forward_demodulation,[],[f863,f381]) ).
fof(f863,plain,
( nil = sK21
| tl(sK21) = sK27(sK21) ),
inference(resolution,[],[f473,f380]) ).
fof(f580,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f1077,plain,
sK23 = tl(cons(sK70,sK23)),
inference(resolution,[],[f933,f607]) ).
fof(f1076,plain,
sK23 = tl(cons(sK69,sK23)),
inference(resolution,[],[f933,f606]) ).
fof(f1075,plain,
! [X0] :
( sK23 = tl(cons(sK60(X0),sK23))
| sP16(X0) ),
inference(resolution,[],[f933,f550]) ).
fof(f1074,plain,
! [X0] :
( sK23 = tl(cons(sK59(X0),sK23))
| sP16(X0) ),
inference(resolution,[],[f933,f549]) ).
fof(f1073,plain,
! [X0] :
( sK23 = tl(cons(sK55(X0),sK23))
| sP14(X0) ),
inference(resolution,[],[f933,f539]) ).
fof(f1072,plain,
! [X0] :
( sK23 = tl(cons(sK54(X0),sK23))
| sP14(X0) ),
inference(resolution,[],[f933,f538]) ).
fof(f1071,plain,
! [X0] :
( sK23 = tl(cons(sK50(X0),sK23))
| sP12(X0) ),
inference(resolution,[],[f933,f528]) ).
fof(f1070,plain,
! [X0] :
( sK23 = tl(cons(sK49(X0),sK23))
| sP12(X0) ),
inference(resolution,[],[f933,f527]) ).
fof(f1069,plain,
! [X0] :
( sK23 = tl(cons(sK45(X0),sK23))
| sP10(X0) ),
inference(resolution,[],[f933,f516]) ).
fof(f1068,plain,
! [X0] :
( sK23 = tl(cons(sK44(X0),sK23))
| sP10(X0) ),
inference(resolution,[],[f933,f515]) ).
fof(f1067,plain,
! [X0] :
( sK23 = tl(cons(sK40(X0),sK23))
| sP8(X0) ),
inference(resolution,[],[f933,f504]) ).
fof(f1066,plain,
! [X0] :
( sK23 = tl(cons(sK39(X0),sK23))
| sP8(X0) ),
inference(resolution,[],[f933,f503]) ).
fof(f1065,plain,
! [X0] :
( sK23 = tl(cons(sK35(X0),sK23))
| sP6(X0) ),
inference(resolution,[],[f933,f492]) ).
fof(f1064,plain,
! [X0] :
( sK23 = tl(cons(sK34(X0),sK23))
| sP6(X0) ),
inference(resolution,[],[f933,f491]) ).
fof(f1063,plain,
! [X0] :
( sK23 = tl(cons(sK30(X0),sK23))
| sP4(X0) ),
inference(resolution,[],[f933,f481]) ).
fof(f1062,plain,
! [X0] :
( sK23 = tl(cons(sK29(X0),sK23))
| sP4(X0) ),
inference(resolution,[],[f933,f480]) ).
fof(f1061,plain,
! [X0] :
( sK23 = tl(cons(sK28(X0),sK23))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f933,f474]) ).
fof(f1060,plain,
! [X0] :
( sK23 = tl(cons(sK26(X0),sK23))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f933,f470]) ).
fof(f1059,plain,
! [X0] :
( sK23 = tl(cons(sK25(X0),sK23))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f933,f465]) ).
fof(f1058,plain,
! [X0] :
( sK23 = tl(cons(hd(X0),sK23))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f933,f467]) ).
fof(f933,plain,
! [X0] :
( ~ ssItem(X0)
| sK23 = tl(cons(X0,sK23)) ),
inference(resolution,[],[f565,f385]) ).
fof(f1055,plain,
sK22 = tl(cons(sK70,sK22)),
inference(resolution,[],[f932,f607]) ).
fof(f1054,plain,
sK22 = tl(cons(sK69,sK22)),
inference(resolution,[],[f932,f606]) ).
fof(f1053,plain,
! [X0] :
( sK22 = tl(cons(sK60(X0),sK22))
| sP16(X0) ),
inference(resolution,[],[f932,f550]) ).
fof(f1052,plain,
! [X0] :
( sK22 = tl(cons(sK59(X0),sK22))
| sP16(X0) ),
inference(resolution,[],[f932,f549]) ).
fof(f1051,plain,
! [X0] :
( sK22 = tl(cons(sK55(X0),sK22))
| sP14(X0) ),
inference(resolution,[],[f932,f539]) ).
fof(f1050,plain,
! [X0] :
( sK22 = tl(cons(sK54(X0),sK22))
| sP14(X0) ),
inference(resolution,[],[f932,f538]) ).
fof(f1049,plain,
! [X0] :
( sK22 = tl(cons(sK50(X0),sK22))
| sP12(X0) ),
inference(resolution,[],[f932,f528]) ).
fof(f1048,plain,
! [X0] :
( sK22 = tl(cons(sK49(X0),sK22))
| sP12(X0) ),
inference(resolution,[],[f932,f527]) ).
fof(f1047,plain,
! [X0] :
( sK22 = tl(cons(sK45(X0),sK22))
| sP10(X0) ),
inference(resolution,[],[f932,f516]) ).
fof(f1046,plain,
! [X0] :
( sK22 = tl(cons(sK44(X0),sK22))
| sP10(X0) ),
inference(resolution,[],[f932,f515]) ).
fof(f1045,plain,
! [X0] :
( sK22 = tl(cons(sK40(X0),sK22))
| sP8(X0) ),
inference(resolution,[],[f932,f504]) ).
fof(f1044,plain,
! [X0] :
( sK22 = tl(cons(sK39(X0),sK22))
| sP8(X0) ),
inference(resolution,[],[f932,f503]) ).
fof(f1043,plain,
! [X0] :
( sK22 = tl(cons(sK35(X0),sK22))
| sP6(X0) ),
inference(resolution,[],[f932,f492]) ).
fof(f1042,plain,
! [X0] :
( sK22 = tl(cons(sK34(X0),sK22))
| sP6(X0) ),
inference(resolution,[],[f932,f491]) ).
fof(f1041,plain,
! [X0] :
( sK22 = tl(cons(sK30(X0),sK22))
| sP4(X0) ),
inference(resolution,[],[f932,f481]) ).
fof(f1040,plain,
! [X0] :
( sK22 = tl(cons(sK29(X0),sK22))
| sP4(X0) ),
inference(resolution,[],[f932,f480]) ).
fof(f1039,plain,
! [X0] :
( sK22 = tl(cons(sK28(X0),sK22))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f932,f474]) ).
fof(f1038,plain,
! [X0] :
( sK22 = tl(cons(sK26(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f932,f470]) ).
fof(f1037,plain,
! [X0] :
( sK22 = tl(cons(sK25(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f932,f465]) ).
fof(f1036,plain,
! [X0] :
( sK22 = tl(cons(hd(X0),sK22))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f932,f467]) ).
fof(f932,plain,
! [X0] :
( ~ ssItem(X0)
| sK22 = tl(cons(X0,sK22)) ),
inference(resolution,[],[f565,f384]) ).
fof(f1033,plain,
sK19 = tl(cons(sK70,sK19)),
inference(resolution,[],[f929,f607]) ).
fof(f1032,plain,
sK19 = tl(cons(sK69,sK19)),
inference(resolution,[],[f929,f606]) ).
fof(f1031,plain,
! [X0] :
( sK19 = tl(cons(sK60(X0),sK19))
| sP16(X0) ),
inference(resolution,[],[f929,f550]) ).
fof(f1030,plain,
! [X0] :
( sK19 = tl(cons(sK59(X0),sK19))
| sP16(X0) ),
inference(resolution,[],[f929,f549]) ).
fof(f1029,plain,
! [X0] :
( sK19 = tl(cons(sK55(X0),sK19))
| sP14(X0) ),
inference(resolution,[],[f929,f539]) ).
fof(f1028,plain,
! [X0] :
( sK19 = tl(cons(sK54(X0),sK19))
| sP14(X0) ),
inference(resolution,[],[f929,f538]) ).
fof(f1027,plain,
! [X0] :
( sK19 = tl(cons(sK50(X0),sK19))
| sP12(X0) ),
inference(resolution,[],[f929,f528]) ).
fof(f1026,plain,
! [X0] :
( sK19 = tl(cons(sK49(X0),sK19))
| sP12(X0) ),
inference(resolution,[],[f929,f527]) ).
fof(f1025,plain,
! [X0] :
( sK19 = tl(cons(sK45(X0),sK19))
| sP10(X0) ),
inference(resolution,[],[f929,f516]) ).
fof(f1024,plain,
! [X0] :
( sK19 = tl(cons(sK44(X0),sK19))
| sP10(X0) ),
inference(resolution,[],[f929,f515]) ).
fof(f1023,plain,
! [X0] :
( sK19 = tl(cons(sK40(X0),sK19))
| sP8(X0) ),
inference(resolution,[],[f929,f504]) ).
fof(f1022,plain,
! [X0] :
( sK19 = tl(cons(sK39(X0),sK19))
| sP8(X0) ),
inference(resolution,[],[f929,f503]) ).
fof(f1021,plain,
! [X0] :
( sK19 = tl(cons(sK35(X0),sK19))
| sP6(X0) ),
inference(resolution,[],[f929,f492]) ).
fof(f1020,plain,
! [X0] :
( sK19 = tl(cons(sK34(X0),sK19))
| sP6(X0) ),
inference(resolution,[],[f929,f491]) ).
fof(f1019,plain,
! [X0] :
( sK19 = tl(cons(sK30(X0),sK19))
| sP4(X0) ),
inference(resolution,[],[f929,f481]) ).
fof(f1018,plain,
! [X0] :
( sK19 = tl(cons(sK29(X0),sK19))
| sP4(X0) ),
inference(resolution,[],[f929,f480]) ).
fof(f1017,plain,
! [X0] :
( sK19 = tl(cons(sK28(X0),sK19))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f929,f474]) ).
fof(f1016,plain,
! [X0] :
( sK19 = tl(cons(sK26(X0),sK19))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f929,f470]) ).
fof(f1015,plain,
! [X0] :
( sK19 = tl(cons(sK25(X0),sK19))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f929,f465]) ).
fof(f1014,plain,
! [X0] :
( sK19 = tl(cons(hd(X0),sK19))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f929,f467]) ).
fof(f929,plain,
! [X0] :
( ~ ssItem(X0)
| sK19 = tl(cons(X0,sK19)) ),
inference(resolution,[],[f565,f378]) ).
fof(f1011,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK62(X1))) = X0
| sP16(X1) ),
inference(resolution,[],[f566,f552]) ).
fof(f1010,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK61(X1))) = X0
| sP16(X1) ),
inference(resolution,[],[f566,f551]) ).
fof(f1009,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK58(X1))) = X0
| sP14(X1) ),
inference(resolution,[],[f566,f542]) ).
fof(f1008,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK57(X1))) = X0
| sP14(X1) ),
inference(resolution,[],[f566,f541]) ).
fof(f1007,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK56(X1))) = X0
| sP14(X1) ),
inference(resolution,[],[f566,f540]) ).
fof(f1006,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK53(X1))) = X0
| sP12(X1) ),
inference(resolution,[],[f566,f531]) ).
fof(f1005,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK52(X1))) = X0
| sP12(X1) ),
inference(resolution,[],[f566,f530]) ).
fof(f1004,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK51(X1))) = X0
| sP12(X1) ),
inference(resolution,[],[f566,f529]) ).
fof(f1003,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK48(X1))) = X0
| sP10(X1) ),
inference(resolution,[],[f566,f519]) ).
fof(f1002,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK47(X1))) = X0
| sP10(X1) ),
inference(resolution,[],[f566,f518]) ).
fof(f1001,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK46(X1))) = X0
| sP10(X1) ),
inference(resolution,[],[f566,f517]) ).
fof(f1000,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK43(X1))) = X0
| sP8(X1) ),
inference(resolution,[],[f566,f507]) ).
fof(f999,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK42(X1))) = X0
| sP8(X1) ),
inference(resolution,[],[f566,f506]) ).
fof(f998,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK41(X1))) = X0
| sP8(X1) ),
inference(resolution,[],[f566,f505]) ).
fof(f997,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK38(X1))) = X0
| sP6(X1) ),
inference(resolution,[],[f566,f495]) ).
fof(f996,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK37(X1))) = X0
| sP6(X1) ),
inference(resolution,[],[f566,f494]) ).
fof(f995,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK36(X1))) = X0
| sP6(X1) ),
inference(resolution,[],[f566,f493]) ).
fof(f994,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK33(X1))) = X0
| sP4(X1) ),
inference(resolution,[],[f566,f484]) ).
fof(f993,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK32(X1))) = X0
| sP4(X1) ),
inference(resolution,[],[f566,f483]) ).
fof(f992,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK31(X1))) = X0
| sP4(X1) ),
inference(resolution,[],[f566,f482]) ).
fof(f991,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK27(X1))) = X0
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f566,f472]) ).
fof(f990,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,sK24(X1))) = X0
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f566,f464]) ).
fof(f989,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK23)) = X0 ),
inference(resolution,[],[f566,f385]) ).
fof(f988,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK22)) = X0 ),
inference(resolution,[],[f566,f384]) ).
fof(f1013,plain,
! [X0] :
( hd(cons(X0,sK19)) = X0
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f987,f381]) ).
fof(f987,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 ),
inference(resolution,[],[f566,f380]) ).
fof(f1012,plain,
! [X0] :
( hd(cons(X0,sK18)) = X0
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f986,f382]) ).
fof(f986,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 ),
inference(resolution,[],[f566,f379]) ).
fof(f985,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK19)) = X0 ),
inference(resolution,[],[f566,f378]) ).
fof(f984,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK18)) = X0 ),
inference(resolution,[],[f566,f377]) ).
fof(f983,plain,
! [X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,tl(X1))) = X0
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f566,f468]) ).
fof(f982,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,nil)) = X0 ),
inference(resolution,[],[f566,f400]) ).
fof(f981,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,app(X1,X2))) = X0
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(resolution,[],[f566,f572]) ).
fof(f980,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| hd(cons(X0,cons(X1,X2))) = X0
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(resolution,[],[f566,f562]) ).
fof(f566,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f977,plain,
sK18 = tl(cons(sK70,sK18)),
inference(resolution,[],[f928,f607]) ).
fof(f976,plain,
sK18 = tl(cons(sK69,sK18)),
inference(resolution,[],[f928,f606]) ).
fof(f975,plain,
! [X0] :
( sK18 = tl(cons(sK60(X0),sK18))
| sP16(X0) ),
inference(resolution,[],[f928,f550]) ).
fof(f974,plain,
! [X0] :
( sK18 = tl(cons(sK59(X0),sK18))
| sP16(X0) ),
inference(resolution,[],[f928,f549]) ).
fof(f973,plain,
! [X0] :
( sK18 = tl(cons(sK55(X0),sK18))
| sP14(X0) ),
inference(resolution,[],[f928,f539]) ).
fof(f972,plain,
! [X0] :
( sK18 = tl(cons(sK54(X0),sK18))
| sP14(X0) ),
inference(resolution,[],[f928,f538]) ).
fof(f971,plain,
! [X0] :
( sK18 = tl(cons(sK50(X0),sK18))
| sP12(X0) ),
inference(resolution,[],[f928,f528]) ).
fof(f970,plain,
! [X0] :
( sK18 = tl(cons(sK49(X0),sK18))
| sP12(X0) ),
inference(resolution,[],[f928,f527]) ).
fof(f969,plain,
! [X0] :
( sK18 = tl(cons(sK45(X0),sK18))
| sP10(X0) ),
inference(resolution,[],[f928,f516]) ).
fof(f968,plain,
! [X0] :
( sK18 = tl(cons(sK44(X0),sK18))
| sP10(X0) ),
inference(resolution,[],[f928,f515]) ).
fof(f967,plain,
! [X0] :
( sK18 = tl(cons(sK40(X0),sK18))
| sP8(X0) ),
inference(resolution,[],[f928,f504]) ).
fof(f966,plain,
! [X0] :
( sK18 = tl(cons(sK39(X0),sK18))
| sP8(X0) ),
inference(resolution,[],[f928,f503]) ).
fof(f965,plain,
! [X0] :
( sK18 = tl(cons(sK35(X0),sK18))
| sP6(X0) ),
inference(resolution,[],[f928,f492]) ).
fof(f964,plain,
! [X0] :
( sK18 = tl(cons(sK34(X0),sK18))
| sP6(X0) ),
inference(resolution,[],[f928,f491]) ).
fof(f963,plain,
! [X0] :
( sK18 = tl(cons(sK30(X0),sK18))
| sP4(X0) ),
inference(resolution,[],[f928,f481]) ).
fof(f962,plain,
! [X0] :
( sK18 = tl(cons(sK29(X0),sK18))
| sP4(X0) ),
inference(resolution,[],[f928,f480]) ).
fof(f961,plain,
! [X0] :
( sK18 = tl(cons(sK28(X0),sK18))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f928,f474]) ).
fof(f960,plain,
! [X0] :
( sK18 = tl(cons(sK26(X0),sK18))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f928,f470]) ).
fof(f959,plain,
! [X0] :
( sK18 = tl(cons(sK25(X0),sK18))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f928,f465]) ).
fof(f958,plain,
! [X0] :
( sK18 = tl(cons(hd(X0),sK18))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f928,f467]) ).
fof(f928,plain,
! [X0] :
( ~ ssItem(X0)
| sK18 = tl(cons(X0,sK18)) ),
inference(resolution,[],[f565,f377]) ).
fof(f955,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK62(X1) = tl(cons(X0,sK62(X1)))
| sP16(X1) ),
inference(resolution,[],[f565,f552]) ).
fof(f954,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK61(X1) = tl(cons(X0,sK61(X1)))
| sP16(X1) ),
inference(resolution,[],[f565,f551]) ).
fof(f953,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK58(X1) = tl(cons(X0,sK58(X1)))
| sP14(X1) ),
inference(resolution,[],[f565,f542]) ).
fof(f952,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK57(X1) = tl(cons(X0,sK57(X1)))
| sP14(X1) ),
inference(resolution,[],[f565,f541]) ).
fof(f951,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK56(X1) = tl(cons(X0,sK56(X1)))
| sP14(X1) ),
inference(resolution,[],[f565,f540]) ).
fof(f950,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK53(X1) = tl(cons(X0,sK53(X1)))
| sP12(X1) ),
inference(resolution,[],[f565,f531]) ).
fof(f949,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK52(X1) = tl(cons(X0,sK52(X1)))
| sP12(X1) ),
inference(resolution,[],[f565,f530]) ).
fof(f948,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK51(X1) = tl(cons(X0,sK51(X1)))
| sP12(X1) ),
inference(resolution,[],[f565,f529]) ).
fof(f947,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK48(X1) = tl(cons(X0,sK48(X1)))
| sP10(X1) ),
inference(resolution,[],[f565,f519]) ).
fof(f946,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK47(X1) = tl(cons(X0,sK47(X1)))
| sP10(X1) ),
inference(resolution,[],[f565,f518]) ).
fof(f945,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK46(X1) = tl(cons(X0,sK46(X1)))
| sP10(X1) ),
inference(resolution,[],[f565,f517]) ).
fof(f944,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK43(X1) = tl(cons(X0,sK43(X1)))
| sP8(X1) ),
inference(resolution,[],[f565,f507]) ).
fof(f943,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK42(X1) = tl(cons(X0,sK42(X1)))
| sP8(X1) ),
inference(resolution,[],[f565,f506]) ).
fof(f942,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK41(X1) = tl(cons(X0,sK41(X1)))
| sP8(X1) ),
inference(resolution,[],[f565,f505]) ).
fof(f941,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK38(X1) = tl(cons(X0,sK38(X1)))
| sP6(X1) ),
inference(resolution,[],[f565,f495]) ).
fof(f940,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK37(X1) = tl(cons(X0,sK37(X1)))
| sP6(X1) ),
inference(resolution,[],[f565,f494]) ).
fof(f939,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK36(X1) = tl(cons(X0,sK36(X1)))
| sP6(X1) ),
inference(resolution,[],[f565,f493]) ).
fof(f938,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK33(X1) = tl(cons(X0,sK33(X1)))
| sP4(X1) ),
inference(resolution,[],[f565,f484]) ).
fof(f937,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK32(X1) = tl(cons(X0,sK32(X1)))
| sP4(X1) ),
inference(resolution,[],[f565,f483]) ).
fof(f936,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK31(X1) = tl(cons(X0,sK31(X1)))
| sP4(X1) ),
inference(resolution,[],[f565,f482]) ).
fof(f935,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK27(X1) = tl(cons(X0,sK27(X1)))
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f565,f472]) ).
fof(f934,plain,
! [X0,X1] :
( ~ ssItem(X0)
| sK24(X1) = tl(cons(X0,sK24(X1)))
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f565,f464]) ).
fof(f957,plain,
! [X0] :
( sK19 = tl(cons(X0,sK19))
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f931,f381]) ).
fof(f931,plain,
! [X0] :
( ~ ssItem(X0)
| sK21 = tl(cons(X0,sK21)) ),
inference(resolution,[],[f565,f380]) ).
fof(f956,plain,
! [X0] :
( sK18 = tl(cons(X0,sK18))
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f930,f382]) ).
fof(f930,plain,
! [X0] :
( ~ ssItem(X0)
| sK20 = tl(cons(X0,sK20)) ),
inference(resolution,[],[f565,f379]) ).
fof(f927,plain,
! [X0,X1] :
( ~ ssItem(X0)
| tl(X1) = tl(cons(X0,tl(X1)))
| nil = X1
| ~ ssList(X1) ),
inference(resolution,[],[f565,f468]) ).
fof(f926,plain,
! [X0] :
( ~ ssItem(X0)
| nil = tl(cons(X0,nil)) ),
inference(resolution,[],[f565,f400]) ).
fof(f925,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| app(X1,X2) = tl(cons(X0,app(X1,X2)))
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(resolution,[],[f565,f572]) ).
fof(f924,plain,
! [X2,X0,X1] :
( ~ ssItem(X0)
| cons(X1,X2) = tl(cons(X0,cons(X1,X2)))
| ~ ssItem(X1)
| ~ ssList(X2) ),
inference(resolution,[],[f565,f562]) ).
fof(f565,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f825,plain,
( nil = sK23
| hd(sK23) = sK26(sK23) ),
inference(resolution,[],[f471,f385]) ).
fof(f475,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK28(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f285,f286]) ).
fof(f286,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK28(X0),nil) = X0
& ssItem(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f285,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f824,plain,
( nil = sK22
| hd(sK22) = sK26(sK22) ),
inference(resolution,[],[f471,f384]) ).
fof(f887,plain,
! [X0] :
( nil = sK62(X0)
| tl(sK62(X0)) = sK27(sK62(X0))
| sP16(X0) ),
inference(resolution,[],[f473,f552]) ).
fof(f886,plain,
! [X0] :
( nil = sK61(X0)
| tl(sK61(X0)) = sK27(sK61(X0))
| sP16(X0) ),
inference(resolution,[],[f473,f551]) ).
fof(f885,plain,
! [X0] :
( nil = sK58(X0)
| tl(sK58(X0)) = sK27(sK58(X0))
| sP14(X0) ),
inference(resolution,[],[f473,f542]) ).
fof(f884,plain,
! [X0] :
( nil = sK57(X0)
| tl(sK57(X0)) = sK27(sK57(X0))
| sP14(X0) ),
inference(resolution,[],[f473,f541]) ).
fof(f883,plain,
! [X0] :
( nil = sK56(X0)
| tl(sK56(X0)) = sK27(sK56(X0))
| sP14(X0) ),
inference(resolution,[],[f473,f540]) ).
fof(f882,plain,
! [X0] :
( nil = sK53(X0)
| tl(sK53(X0)) = sK27(sK53(X0))
| sP12(X0) ),
inference(resolution,[],[f473,f531]) ).
fof(f881,plain,
! [X0] :
( nil = sK52(X0)
| tl(sK52(X0)) = sK27(sK52(X0))
| sP12(X0) ),
inference(resolution,[],[f473,f530]) ).
fof(f880,plain,
! [X0] :
( nil = sK51(X0)
| tl(sK51(X0)) = sK27(sK51(X0))
| sP12(X0) ),
inference(resolution,[],[f473,f529]) ).
fof(f879,plain,
! [X0] :
( nil = sK48(X0)
| tl(sK48(X0)) = sK27(sK48(X0))
| sP10(X0) ),
inference(resolution,[],[f473,f519]) ).
fof(f878,plain,
! [X0] :
( nil = sK47(X0)
| tl(sK47(X0)) = sK27(sK47(X0))
| sP10(X0) ),
inference(resolution,[],[f473,f518]) ).
fof(f877,plain,
! [X0] :
( nil = sK46(X0)
| tl(sK46(X0)) = sK27(sK46(X0))
| sP10(X0) ),
inference(resolution,[],[f473,f517]) ).
fof(f876,plain,
! [X0] :
( nil = sK43(X0)
| tl(sK43(X0)) = sK27(sK43(X0))
| sP8(X0) ),
inference(resolution,[],[f473,f507]) ).
fof(f875,plain,
! [X0] :
( nil = sK42(X0)
| tl(sK42(X0)) = sK27(sK42(X0))
| sP8(X0) ),
inference(resolution,[],[f473,f506]) ).
fof(f874,plain,
! [X0] :
( nil = sK41(X0)
| tl(sK41(X0)) = sK27(sK41(X0))
| sP8(X0) ),
inference(resolution,[],[f473,f505]) ).
fof(f873,plain,
! [X0] :
( nil = sK38(X0)
| tl(sK38(X0)) = sK27(sK38(X0))
| sP6(X0) ),
inference(resolution,[],[f473,f495]) ).
fof(f872,plain,
! [X0] :
( nil = sK37(X0)
| tl(sK37(X0)) = sK27(sK37(X0))
| sP6(X0) ),
inference(resolution,[],[f473,f494]) ).
fof(f871,plain,
! [X0] :
( nil = sK36(X0)
| tl(sK36(X0)) = sK27(sK36(X0))
| sP6(X0) ),
inference(resolution,[],[f473,f493]) ).
fof(f870,plain,
! [X0] :
( nil = sK33(X0)
| tl(sK33(X0)) = sK27(sK33(X0))
| sP4(X0) ),
inference(resolution,[],[f473,f484]) ).
fof(f869,plain,
! [X0] :
( nil = sK32(X0)
| tl(sK32(X0)) = sK27(sK32(X0))
| sP4(X0) ),
inference(resolution,[],[f473,f483]) ).
fof(f868,plain,
! [X0] :
( nil = sK31(X0)
| tl(sK31(X0)) = sK27(sK31(X0))
| sP4(X0) ),
inference(resolution,[],[f473,f482]) ).
fof(f867,plain,
! [X0] :
( nil = sK27(X0)
| tl(sK27(X0)) = sK27(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f473,f472]) ).
fof(f866,plain,
! [X0] :
( nil = sK24(X0)
| tl(sK24(X0)) = sK27(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f473,f464]) ).
fof(f865,plain,
( nil = sK23
| tl(sK23) = sK27(sK23) ),
inference(resolution,[],[f473,f385]) ).
fof(f864,plain,
( nil = sK22
| tl(sK22) = sK27(sK22) ),
inference(resolution,[],[f473,f384]) ).
fof(f859,plain,
! [X0] :
( nil = tl(X0)
| tl(tl(X0)) = sK27(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f473,f468]) ).
fof(f857,plain,
! [X0,X1] :
( nil = app(X0,X1)
| tl(app(X0,X1)) = sK27(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f473,f572]) ).
fof(f888,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = sK27(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f856,f563]) ).
fof(f856,plain,
! [X0,X1] :
( nil = cons(X0,X1)
| tl(cons(X0,X1)) = sK27(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(resolution,[],[f473,f562]) ).
fof(f473,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK27(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0] :
( ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f160,f282]) ).
fof(f282,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK27(X0)
& ssList(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
fof(f847,plain,
! [X0] :
( nil = sK62(X0)
| hd(sK62(X0)) = sK26(sK62(X0))
| sP16(X0) ),
inference(resolution,[],[f471,f552]) ).
fof(f846,plain,
! [X0] :
( nil = sK61(X0)
| hd(sK61(X0)) = sK26(sK61(X0))
| sP16(X0) ),
inference(resolution,[],[f471,f551]) ).
fof(f845,plain,
! [X0] :
( nil = sK58(X0)
| hd(sK58(X0)) = sK26(sK58(X0))
| sP14(X0) ),
inference(resolution,[],[f471,f542]) ).
fof(f844,plain,
! [X0] :
( nil = sK57(X0)
| hd(sK57(X0)) = sK26(sK57(X0))
| sP14(X0) ),
inference(resolution,[],[f471,f541]) ).
fof(f843,plain,
! [X0] :
( nil = sK56(X0)
| hd(sK56(X0)) = sK26(sK56(X0))
| sP14(X0) ),
inference(resolution,[],[f471,f540]) ).
fof(f842,plain,
! [X0] :
( nil = sK53(X0)
| hd(sK53(X0)) = sK26(sK53(X0))
| sP12(X0) ),
inference(resolution,[],[f471,f531]) ).
fof(f841,plain,
! [X0] :
( nil = sK52(X0)
| hd(sK52(X0)) = sK26(sK52(X0))
| sP12(X0) ),
inference(resolution,[],[f471,f530]) ).
fof(f840,plain,
! [X0] :
( nil = sK51(X0)
| hd(sK51(X0)) = sK26(sK51(X0))
| sP12(X0) ),
inference(resolution,[],[f471,f529]) ).
fof(f839,plain,
! [X0] :
( nil = sK48(X0)
| hd(sK48(X0)) = sK26(sK48(X0))
| sP10(X0) ),
inference(resolution,[],[f471,f519]) ).
fof(f838,plain,
! [X0] :
( nil = sK47(X0)
| hd(sK47(X0)) = sK26(sK47(X0))
| sP10(X0) ),
inference(resolution,[],[f471,f518]) ).
fof(f837,plain,
! [X0] :
( nil = sK46(X0)
| hd(sK46(X0)) = sK26(sK46(X0))
| sP10(X0) ),
inference(resolution,[],[f471,f517]) ).
fof(f836,plain,
! [X0] :
( nil = sK43(X0)
| hd(sK43(X0)) = sK26(sK43(X0))
| sP8(X0) ),
inference(resolution,[],[f471,f507]) ).
fof(f835,plain,
! [X0] :
( nil = sK42(X0)
| hd(sK42(X0)) = sK26(sK42(X0))
| sP8(X0) ),
inference(resolution,[],[f471,f506]) ).
fof(f834,plain,
! [X0] :
( nil = sK41(X0)
| hd(sK41(X0)) = sK26(sK41(X0))
| sP8(X0) ),
inference(resolution,[],[f471,f505]) ).
fof(f833,plain,
! [X0] :
( nil = sK38(X0)
| hd(sK38(X0)) = sK26(sK38(X0))
| sP6(X0) ),
inference(resolution,[],[f471,f495]) ).
fof(f832,plain,
! [X0] :
( nil = sK37(X0)
| hd(sK37(X0)) = sK26(sK37(X0))
| sP6(X0) ),
inference(resolution,[],[f471,f494]) ).
fof(f831,plain,
! [X0] :
( nil = sK36(X0)
| hd(sK36(X0)) = sK26(sK36(X0))
| sP6(X0) ),
inference(resolution,[],[f471,f493]) ).
fof(f830,plain,
! [X0] :
( nil = sK33(X0)
| hd(sK33(X0)) = sK26(sK33(X0))
| sP4(X0) ),
inference(resolution,[],[f471,f484]) ).
fof(f829,plain,
! [X0] :
( nil = sK32(X0)
| hd(sK32(X0)) = sK26(sK32(X0))
| sP4(X0) ),
inference(resolution,[],[f471,f483]) ).
fof(f828,plain,
! [X0] :
( nil = sK31(X0)
| hd(sK31(X0)) = sK26(sK31(X0))
| sP4(X0) ),
inference(resolution,[],[f471,f482]) ).
fof(f827,plain,
! [X0] :
( nil = sK27(X0)
| hd(sK27(X0)) = sK26(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f471,f472]) ).
fof(f826,plain,
! [X0] :
( nil = sK24(X0)
| hd(sK24(X0)) = sK26(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f471,f464]) ).
fof(f819,plain,
! [X0] :
( nil = tl(X0)
| hd(tl(X0)) = sK26(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[],[f471,f468]) ).
fof(f817,plain,
! [X0,X1] :
( nil = app(X0,X1)
| hd(app(X0,X1)) = sK26(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f471,f572]) ).
fof(f848,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = sK26(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f816,f563]) ).
fof(f816,plain,
! [X0,X1] :
( nil = cons(X0,X1)
| hd(cons(X0,X1)) = sK26(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(resolution,[],[f471,f562]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK26(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f158,f280]) ).
fof(f280,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK26(X0)
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
fof(f815,plain,
! [X0,X1] :
( nil = X0
| ~ sP2(X0,X1)
| ~ lt(hd(X0),X1)
| ~ ssItem(X1)
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f449,f414]) ).
fof(f814,plain,
! [X0,X1] :
( nil = X0
| ~ sP2(X0,X1)
| leq(X1,hd(X0))
| ~ ssItem(hd(X0))
| ~ ssItem(X1) ),
inference(resolution,[],[f449,f424]) ).
fof(f813,plain,
! [X0] :
( nil = X0
| ~ sP2(X0,hd(X0))
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f449,f402]) ).
fof(f449,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f273]) ).
fof(f273,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f272]) ).
fof(f272,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f446,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f445,plain,
! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f441,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f269]) ).
fof(f269,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f438,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f437,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f424,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f261]) ).
fof(f261,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).
fof(f422,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( geq(X0,X1)
<=> leq(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( geq(X0,X1)
<=> leq(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
fof(f421,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f801,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X0,X1) ),
inference(duplicate_literal_removal,[],[f800]) ).
fof(f800,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[],[f420,f412]) ).
fof(f420,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( gt(X0,X1)
<=> lt(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
<=> lt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
fof(f419,plain,
! [X0,X1] :
( ~ gt(X0,X1)
| lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f731,plain,
! [X0] :
( sP16(X0)
| sK62(X0) = app(nil,sK62(X0)) ),
inference(resolution,[],[f463,f552]) ).
fof(f730,plain,
! [X0] :
( sP16(X0)
| sK61(X0) = app(nil,sK61(X0)) ),
inference(resolution,[],[f463,f551]) ).
fof(f798,plain,
! [X0] :
( sK58(X0) = app(nil,sK58(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f729,f670]) ).
fof(f729,plain,
! [X0] :
( sP14(X0)
| sK58(X0) = app(nil,sK58(X0)) ),
inference(resolution,[],[f463,f542]) ).
fof(f797,plain,
! [X0] :
( sK57(X0) = app(nil,sK57(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f728,f670]) ).
fof(f728,plain,
! [X0] :
( sP14(X0)
| sK57(X0) = app(nil,sK57(X0)) ),
inference(resolution,[],[f463,f541]) ).
fof(f796,plain,
! [X0] :
( sK56(X0) = app(nil,sK56(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f727,f670]) ).
fof(f727,plain,
! [X0] :
( sP14(X0)
| sK56(X0) = app(nil,sK56(X0)) ),
inference(resolution,[],[f463,f540]) ).
fof(f795,plain,
! [X0] :
( sK53(X0) = app(nil,sK53(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f726,f668]) ).
fof(f726,plain,
! [X0] :
( sP12(X0)
| sK53(X0) = app(nil,sK53(X0)) ),
inference(resolution,[],[f463,f531]) ).
fof(f794,plain,
! [X0] :
( sK52(X0) = app(nil,sK52(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f725,f668]) ).
fof(f725,plain,
! [X0] :
( sP12(X0)
| sK52(X0) = app(nil,sK52(X0)) ),
inference(resolution,[],[f463,f530]) ).
fof(f793,plain,
! [X0] :
( sK51(X0) = app(nil,sK51(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f724,f668]) ).
fof(f724,plain,
! [X0] :
( sP12(X0)
| sK51(X0) = app(nil,sK51(X0)) ),
inference(resolution,[],[f463,f529]) ).
fof(f418,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f723,plain,
! [X0] :
( sP10(X0)
| sK48(X0) = app(nil,sK48(X0)) ),
inference(resolution,[],[f463,f519]) ).
fof(f722,plain,
! [X0] :
( sP10(X0)
| sK47(X0) = app(nil,sK47(X0)) ),
inference(resolution,[],[f463,f518]) ).
fof(f721,plain,
! [X0] :
( sP10(X0)
| sK46(X0) = app(nil,sK46(X0)) ),
inference(resolution,[],[f463,f517]) ).
fof(f720,plain,
! [X0] :
( sP8(X0)
| sK43(X0) = app(nil,sK43(X0)) ),
inference(resolution,[],[f463,f507]) ).
fof(f719,plain,
! [X0] :
( sP8(X0)
| sK42(X0) = app(nil,sK42(X0)) ),
inference(resolution,[],[f463,f506]) ).
fof(f718,plain,
! [X0] :
( sP8(X0)
| sK41(X0) = app(nil,sK41(X0)) ),
inference(resolution,[],[f463,f505]) ).
fof(f717,plain,
! [X0] :
( sP6(X0)
| sK38(X0) = app(nil,sK38(X0)) ),
inference(resolution,[],[f463,f495]) ).
fof(f716,plain,
! [X0] :
( sP6(X0)
| sK37(X0) = app(nil,sK37(X0)) ),
inference(resolution,[],[f463,f494]) ).
fof(f715,plain,
! [X0] :
( sP6(X0)
| sK36(X0) = app(nil,sK36(X0)) ),
inference(resolution,[],[f463,f493]) ).
fof(f714,plain,
! [X0] :
( sP4(X0)
| sK33(X0) = app(nil,sK33(X0)) ),
inference(resolution,[],[f463,f484]) ).
fof(f713,plain,
! [X0] :
( sP4(X0)
| sK32(X0) = app(nil,sK32(X0)) ),
inference(resolution,[],[f463,f483]) ).
fof(f414,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
=> ~ lt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
fof(f712,plain,
! [X0] :
( sP4(X0)
| sK31(X0) = app(nil,sK31(X0)) ),
inference(resolution,[],[f463,f482]) ).
fof(f702,plain,
! [X0] :
( sP16(X0)
| sK62(X0) = app(sK62(X0),nil) ),
inference(resolution,[],[f462,f552]) ).
fof(f701,plain,
! [X0] :
( sP16(X0)
| sK61(X0) = app(sK61(X0),nil) ),
inference(resolution,[],[f462,f551]) ).
fof(f777,plain,
! [X0] :
( sK58(X0) = app(sK58(X0),nil)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f700,f670]) ).
fof(f700,plain,
! [X0] :
( sP14(X0)
| sK58(X0) = app(sK58(X0),nil) ),
inference(resolution,[],[f462,f542]) ).
fof(f776,plain,
! [X0] :
( sK57(X0) = app(sK57(X0),nil)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f699,f670]) ).
fof(f699,plain,
! [X0] :
( sP14(X0)
| sK57(X0) = app(sK57(X0),nil) ),
inference(resolution,[],[f462,f541]) ).
fof(f775,plain,
! [X0] :
( sK56(X0) = app(sK56(X0),nil)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f698,f670]) ).
fof(f698,plain,
! [X0] :
( sP14(X0)
| sK56(X0) = app(sK56(X0),nil) ),
inference(resolution,[],[f462,f540]) ).
fof(f774,plain,
! [X0] :
( sK53(X0) = app(sK53(X0),nil)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f697,f668]) ).
fof(f697,plain,
! [X0] :
( sP12(X0)
| sK53(X0) = app(sK53(X0),nil) ),
inference(resolution,[],[f462,f531]) ).
fof(f773,plain,
! [X0] :
( sK52(X0) = app(sK52(X0),nil)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f696,f668]) ).
fof(f696,plain,
! [X0] :
( sP12(X0)
| sK52(X0) = app(sK52(X0),nil) ),
inference(resolution,[],[f462,f530]) ).
fof(f772,plain,
! [X0] :
( sK51(X0) = app(sK51(X0),nil)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f695,f668]) ).
fof(f695,plain,
! [X0] :
( sP12(X0)
| sK51(X0) = app(sK51(X0),nil) ),
inference(resolution,[],[f462,f529]) ).
fof(f694,plain,
! [X0] :
( sP10(X0)
| sK48(X0) = app(sK48(X0),nil) ),
inference(resolution,[],[f462,f519]) ).
fof(f693,plain,
! [X0] :
( sP10(X0)
| sK47(X0) = app(sK47(X0),nil) ),
inference(resolution,[],[f462,f518]) ).
fof(f412,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
=> ~ gt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).
fof(f692,plain,
! [X0] :
( sP10(X0)
| sK46(X0) = app(sK46(X0),nil) ),
inference(resolution,[],[f462,f517]) ).
fof(f691,plain,
! [X0] :
( sP8(X0)
| sK43(X0) = app(sK43(X0),nil) ),
inference(resolution,[],[f462,f507]) ).
fof(f690,plain,
! [X0] :
( sP8(X0)
| sK42(X0) = app(sK42(X0),nil) ),
inference(resolution,[],[f462,f506]) ).
fof(f689,plain,
! [X0] :
( sP8(X0)
| sK41(X0) = app(sK41(X0),nil) ),
inference(resolution,[],[f462,f505]) ).
fof(f688,plain,
! [X0] :
( sP6(X0)
| sK38(X0) = app(sK38(X0),nil) ),
inference(resolution,[],[f462,f495]) ).
fof(f687,plain,
! [X0] :
( sP6(X0)
| sK37(X0) = app(sK37(X0),nil) ),
inference(resolution,[],[f462,f494]) ).
fof(f686,plain,
! [X0] :
( sP6(X0)
| sK36(X0) = app(sK36(X0),nil) ),
inference(resolution,[],[f462,f493]) ).
fof(f685,plain,
! [X0] :
( sP4(X0)
| sK33(X0) = app(sK33(X0),nil) ),
inference(resolution,[],[f462,f484]) ).
fof(f684,plain,
! [X0] :
( sP4(X0)
| sK32(X0) = app(sK32(X0),nil) ),
inference(resolution,[],[f462,f483]) ).
fof(f683,plain,
! [X0] :
( sP4(X0)
| sK31(X0) = app(sK31(X0),nil) ),
inference(resolution,[],[f462,f482]) ).
fof(f640,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f611]) ).
fof(f611,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f432]) ).
fof(f432,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f263]) ).
fof(f263,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f564,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f563,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f760,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X0) = app(app(X1,X0),nil) ),
inference(resolution,[],[f572,f462]) ).
fof(f759,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X0) = app(nil,app(X1,X0)) ),
inference(resolution,[],[f572,f463]) ).
fof(f572,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f758,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(cons(X0,X1),nil) ),
inference(resolution,[],[f562,f462]) ).
fof(f757,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| cons(X0,X1) = app(nil,cons(X0,X1)) ),
inference(resolution,[],[f562,f463]) ).
fof(f562,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f560,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f558,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f556,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f741,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK27(X0) = app(sK27(X0),nil) ),
inference(resolution,[],[f472,f462]) ).
fof(f740,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK27(X0) = app(nil,sK27(X0)) ),
inference(resolution,[],[f472,f463]) ).
fof(f472,plain,
! [X0] :
( ssList(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f470,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f739,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| tl(X0) = app(tl(X0),nil) ),
inference(resolution,[],[f468,f462]) ).
fof(f738,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| tl(X0) = app(nil,tl(X0)) ),
inference(resolution,[],[f468,f463]) ).
fof(f468,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f467,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f465,plain,
! [X0] :
( ssItem(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0] :
( ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0))
& ssList(sK24(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f150,f278,f277]) ).
fof(f277,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
& ssList(sK24(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f278,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK24(X0)) = X0
& ssItem(X2) )
=> ( cons(sK25(X0),sK24(X0)) = X0
& ssItem(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f737,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK24(X0) = app(sK24(X0),nil) ),
inference(resolution,[],[f464,f462]) ).
fof(f736,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| sK24(X0) = app(nil,sK24(X0)) ),
inference(resolution,[],[f464,f463]) ).
fof(f464,plain,
! [X0] :
( ssList(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f448,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f274]) ).
fof(f440,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f554,plain,
! [X0] :
( sK59(X0) != sK60(X0)
| sP16(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0] :
( ( sP16(X0)
| ( sK59(X0) != sK60(X0)
& app(sK61(X0),cons(sK59(X0),cons(sK60(X0),sK62(X0)))) = X0
& ssList(sK62(X0))
& ssList(sK61(X0))
& ssItem(sK60(X0))
& ssItem(sK59(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP16(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61,sK62])],[f344,f348,f347,f346,f345]) ).
fof(f345,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK59(X0) != X2
& app(X3,cons(sK59(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f346,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK59(X0) != X2
& app(X3,cons(sK59(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK59(X0) != sK60(X0)
& app(X3,cons(sK59(X0),cons(sK60(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK59(X0) != sK60(X0)
& app(X3,cons(sK59(X0),cons(sK60(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK59(X0) != sK60(X0)
& app(sK61(X0),cons(sK59(X0),cons(sK60(X0),X4))) = X0
& ssList(X4) )
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ? [X4] :
( sK59(X0) != sK60(X0)
& app(sK61(X0),cons(sK59(X0),cons(sK60(X0),X4))) = X0
& ssList(X4) )
=> ( sK59(X0) != sK60(X0)
& app(sK61(X0),cons(sK59(X0),cons(sK60(X0),sK62(X0)))) = X0
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ( sP16(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP16(X0) ) ),
inference(rectify,[],[f343]) ).
fof(f343,plain,
! [X0] :
( ( sP16(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP16(X0) ) ),
inference(nnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0] :
( sP16(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f544,plain,
! [X0] :
( ~ lt(sK54(X0),sK55(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f341,plain,
! [X0] :
( ( sP14(X0)
| ( ~ lt(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0
& ssList(sK58(X0))
& ssList(sK57(X0))
& ssList(sK56(X0))
& ssItem(sK55(X0))
& ssItem(sK54(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP14(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56,sK57,sK58])],[f335,f340,f339,f338,f337,f336]) ).
fof(f336,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK54(X0),X2)
& app(app(X3,cons(sK54(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f337,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK54(X0),X2)
& app(app(X3,cons(sK54(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK54(X0),sK55(X0))
& app(app(X3,cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f338,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK54(X0),sK55(X0))
& app(app(X3,cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f340,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0
& ssList(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( ( sP14(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP14(X0) ) ),
inference(rectify,[],[f334]) ).
fof(f334,plain,
! [X0] :
( ( sP14(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP14(X0) ) ),
inference(nnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( sP14(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f533,plain,
! [X0] :
( ~ leq(sK49(X0),sK50(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f332,plain,
! [X0] :
( ( sP12(X0)
| ( ~ leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0
& ssList(sK53(X0))
& ssList(sK52(X0))
& ssList(sK51(X0))
& ssItem(sK50(X0))
& ssItem(sK49(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP12(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52,sK53])],[f326,f331,f330,f329,f328,f327]) ).
fof(f327,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK49(X0),X2)
& app(app(X3,cons(sK49(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f328,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK49(X0),X2)
& app(app(X3,cons(sK49(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK49(X0),sK50(X0))
& app(app(X3,cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f329,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK49(X0),sK50(X0))
& app(app(X3,cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f331,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0
& ssList(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ( sP12(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP12(X0) ) ),
inference(rectify,[],[f325]) ).
fof(f325,plain,
! [X0] :
( ( sP12(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP12(X0) ) ),
inference(nnf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0] :
( sP12(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f522,plain,
! [X0] :
( leq(sK45(X0),sK44(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0] :
( ( sP10(X0)
| ( leq(sK45(X0),sK44(X0))
& leq(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0
& ssList(sK48(X0))
& ssList(sK47(X0))
& ssList(sK46(X0))
& ssItem(sK45(X0))
& ssItem(sK44(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP10(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46,sK47,sK48])],[f317,f322,f321,f320,f319,f318]) ).
fof(f318,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK44(X0))
& leq(sK44(X0),X2)
& app(app(X3,cons(sK44(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f319,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK44(X0))
& leq(sK44(X0),X2)
& app(app(X3,cons(sK44(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK45(X0),sK44(X0))
& leq(sK44(X0),sK45(X0))
& app(app(X3,cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f320,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK45(X0),sK44(X0))
& leq(sK44(X0),sK45(X0))
& app(app(X3,cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK45(X0),sK44(X0))
& leq(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK45(X0),sK44(X0))
& leq(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK45(X0),sK44(X0))
& leq(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f322,plain,
! [X0] :
( ? [X5] :
( leq(sK45(X0),sK44(X0))
& leq(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK45(X0),sK44(X0))
& leq(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0
& ssList(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0] :
( ( sP10(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP10(X0) ) ),
inference(rectify,[],[f316]) ).
fof(f316,plain,
! [X0] :
( ( sP10(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP10(X0) ) ),
inference(nnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0] :
( sP10(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f521,plain,
! [X0] :
( leq(sK44(X0),sK45(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f510,plain,
! [X0] :
( ~ lt(sK40(X0),sK39(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f314,plain,
! [X0] :
( ( sP8(X0)
| ( ~ lt(sK40(X0),sK39(X0))
& ~ lt(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0
& ssList(sK43(X0))
& ssList(sK42(X0))
& ssList(sK41(X0))
& ssItem(sK40(X0))
& ssItem(sK39(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP8(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40,sK41,sK42,sK43])],[f308,f313,f312,f311,f310,f309]) ).
fof(f309,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK39(X0))
& ~ lt(sK39(X0),X2)
& app(app(X3,cons(sK39(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f310,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK39(X0))
& ~ lt(sK39(X0),X2)
& app(app(X3,cons(sK39(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK40(X0),sK39(X0))
& ~ lt(sK39(X0),sK40(X0))
& app(app(X3,cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f311,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK40(X0),sK39(X0))
& ~ lt(sK39(X0),sK40(X0))
& app(app(X3,cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK40(X0),sK39(X0))
& ~ lt(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK40(X0),sK39(X0))
& ~ lt(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK40(X0),sK39(X0))
& ~ lt(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f313,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK40(X0),sK39(X0))
& ~ lt(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK40(X0),sK39(X0))
& ~ lt(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0
& ssList(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP8(X0) ) ),
inference(rectify,[],[f307]) ).
fof(f307,plain,
! [X0] :
( ( sP8(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP8(X0) ) ),
inference(nnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( sP8(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f509,plain,
! [X0] :
( ~ lt(sK39(X0),sK40(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f498,plain,
! [X0] :
( ~ leq(sK35(X0),sK34(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0] :
( ( sP6(X0)
| ( ~ leq(sK35(X0),sK34(X0))
& ~ leq(sK34(X0),sK35(X0))
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0
& ssList(sK38(X0))
& ssList(sK37(X0))
& ssList(sK36(X0))
& ssItem(sK35(X0))
& ssItem(sK34(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37,sK38])],[f299,f304,f303,f302,f301,f300]) ).
fof(f300,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK34(X0))
& ~ leq(sK34(X0),X2)
& app(app(X3,cons(sK34(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f301,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK34(X0))
& ~ leq(sK34(X0),X2)
& app(app(X3,cons(sK34(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK35(X0),sK34(X0))
& ~ leq(sK34(X0),sK35(X0))
& app(app(X3,cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f302,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK35(X0),sK34(X0))
& ~ leq(sK34(X0),sK35(X0))
& app(app(X3,cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK35(X0),sK34(X0))
& ~ leq(sK34(X0),sK35(X0))
& app(app(sK36(X0),cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK35(X0),sK34(X0))
& ~ leq(sK34(X0),sK35(X0))
& app(app(sK36(X0),cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK35(X0),sK34(X0))
& ~ leq(sK34(X0),sK35(X0))
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f304,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK35(X0),sK34(X0))
& ~ leq(sK34(X0),sK35(X0))
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK35(X0),sK34(X0))
& ~ leq(sK34(X0),sK35(X0))
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0
& ssList(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP6(X0) ) ),
inference(rectify,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ( sP6(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0] :
( sP6(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f497,plain,
! [X0] :
( ~ leq(sK34(X0),sK35(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f486,plain,
! [X0] :
( sP4(X0)
| sK29(X0) = sK30(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f296,plain,
! [X0] :
( ( sP4(X0)
| ( sK29(X0) = sK30(X0)
& app(app(sK31(X0),cons(sK29(X0),sK32(X0))),cons(sK30(X0),sK33(X0))) = X0
& ssList(sK33(X0))
& ssList(sK32(X0))
& ssList(sK31(X0))
& ssItem(sK30(X0))
& ssItem(sK29(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31,sK32,sK33])],[f290,f295,f294,f293,f292,f291]) ).
fof(f291,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK29(X0) = X2
& app(app(X3,cons(sK29(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f292,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK29(X0) = X2
& app(app(X3,cons(sK29(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK29(X0) = sK30(X0)
& app(app(X3,cons(sK29(X0),X4)),cons(sK30(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f293,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK29(X0) = sK30(X0)
& app(app(X3,cons(sK29(X0),X4)),cons(sK30(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK29(X0) = sK30(X0)
& app(app(sK31(X0),cons(sK29(X0),X4)),cons(sK30(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f294,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK29(X0) = sK30(X0)
& app(app(sK31(X0),cons(sK29(X0),X4)),cons(sK30(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK29(X0) = sK30(X0)
& app(app(sK31(X0),cons(sK29(X0),sK32(X0))),cons(sK30(X0),X5)) = X0
& ssList(X5) )
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f295,plain,
! [X0] :
( ? [X5] :
( sK29(X0) = sK30(X0)
& app(app(sK31(X0),cons(sK29(X0),sK32(X0))),cons(sK30(X0),X5)) = X0
& ssList(X5) )
=> ( sK29(X0) = sK30(X0)
& app(app(sK31(X0),cons(sK29(X0),sK32(X0))),cons(sK30(X0),sK33(X0))) = X0
& ssList(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f290,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP4(X0) ) ),
inference(rectify,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0] :
( sP4(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f474,plain,
! [X0] :
( ssItem(sK28(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f711,plain,
sK23 = app(nil,sK23),
inference(resolution,[],[f463,f385]) ).
fof(f710,plain,
sK22 = app(nil,sK22),
inference(resolution,[],[f463,f384]) ).
fof(f707,plain,
sK19 = app(nil,sK19),
inference(resolution,[],[f463,f378]) ).
fof(f706,plain,
sK18 = app(nil,sK18),
inference(resolution,[],[f463,f377]) ).
fof(f682,plain,
sK23 = app(sK23,nil),
inference(resolution,[],[f462,f385]) ).
fof(f681,plain,
sK22 = app(sK22,nil),
inference(resolution,[],[f462,f384]) ).
fof(f733,plain,
sK19 = app(nil,sK19),
inference(forward_demodulation,[],[f709,f381]) ).
fof(f709,plain,
sK21 = app(nil,sK21),
inference(resolution,[],[f463,f380]) ).
fof(f732,plain,
sK18 = app(nil,sK18),
inference(forward_demodulation,[],[f708,f382]) ).
fof(f708,plain,
sK20 = app(nil,sK20),
inference(resolution,[],[f463,f379]) ).
fof(f463,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f678,plain,
sK19 = app(sK19,nil),
inference(resolution,[],[f462,f378]) ).
fof(f677,plain,
sK18 = app(sK18,nil),
inference(resolution,[],[f462,f377]) ).
fof(f704,plain,
sK19 = app(sK19,nil),
inference(forward_demodulation,[],[f680,f381]) ).
fof(f680,plain,
sK21 = app(sK21,nil),
inference(resolution,[],[f462,f380]) ).
fof(f703,plain,
sK18 = app(sK18,nil),
inference(forward_demodulation,[],[f679,f382]) ).
fof(f679,plain,
sK20 = app(sK20,nil),
inference(resolution,[],[f462,f379]) ).
fof(f462,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f452,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f139,f228,f227]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).
fof(f671,plain,
! [X0] :
( sP16(X0)
| ~ equalelemsP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f546,f555]) ).
fof(f670,plain,
! [X0] :
( ~ sP14(X0)
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f536,f545]) ).
fof(f669,plain,
! [X0] :
( sP14(X0)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f535,f545]) ).
fof(f668,plain,
! [X0] :
( ~ sP12(X0)
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f525,f534]) ).
fof(f667,plain,
! [X0] :
( sP12(X0)
| ~ totalorderedP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f524,f534]) ).
fof(f666,plain,
! [X0] :
( sP10(X0)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f512,f523]) ).
fof(f665,plain,
! [X0] :
( sP8(X0)
| ~ strictorderP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f500,f511]) ).
fof(f444,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X0] :
( ! [X1] :
( sP1(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f225,f224]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).
fof(f664,plain,
! [X0] :
( sP6(X0)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f488,f499]) ).
fof(f663,plain,
! [X0] :
( sP4(X0)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f477,f487]) ).
fof(f546,plain,
! [X0] :
( ~ sP17(X0)
| ~ equalelemsP(X0)
| sP16(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f342,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP16(X0) )
& ( sP16(X0)
| ~ equalelemsP(X0) ) )
| ~ sP17(X0) ),
inference(nnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP16(X0) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f536,plain,
! [X0] :
( ~ sP15(X0)
| ~ sP14(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP14(X0) )
& ( sP14(X0)
| ~ strictorderedP(X0) ) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP14(X0) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f535,plain,
! [X0] :
( ~ sP15(X0)
| ~ strictorderedP(X0)
| sP14(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f525,plain,
! [X0] :
( ~ sP13(X0)
| ~ sP12(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f324,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP12(X0) )
& ( sP12(X0)
| ~ totalorderedP(X0) ) )
| ~ sP13(X0) ),
inference(nnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP12(X0) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f524,plain,
! [X0] :
( ~ sP13(X0)
| ~ totalorderedP(X0)
| sP12(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f512,plain,
! [X0] :
( ~ sP11(X0)
| ~ cyclefreeP(X0)
| sP10(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP10(X0) )
& ( sP10(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP11(X0) ),
inference(nnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP10(X0) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f500,plain,
! [X0] :
( ~ sP9(X0)
| ~ strictorderP(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP8(X0) )
& ( sP8(X0)
| ~ strictorderP(X0) ) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP8(X0) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f488,plain,
! [X0] :
( ~ sP7(X0)
| ~ totalorderP(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP6(X0) )
& ( sP6(X0)
| ~ totalorderP(X0) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP6(X0) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f477,plain,
! [X0] :
( ~ sP5(X0)
| ~ duplicatefreeP(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f411,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
fof(f410,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
fof(f409,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f408,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
fof(f407,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
fof(f406,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f405,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ssItem(X0)
=> cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
fof(f662,plain,
sK19 = app(app(sK22,sK18),sK23),
inference(forward_demodulation,[],[f661,f381]) ).
fof(f661,plain,
sK21 = app(app(sK22,sK18),sK23),
inference(forward_demodulation,[],[f386,f382]) ).
fof(f646,plain,
nil = app(nil,nil),
inference(global_subsumption,[],[f391,f390,f389,f388,f387,f386,f385,f384,f383,f382,f381,f380,f379,f378,f377,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f418,f642,f420,f419,f422,f421,f425,f424,f641,f426,f427,f428,f429,f430,f433,f640,f431,f639,f435,f434,f438,f437,f443,f613,f441,f440,f444,f446,f445,f451,f615,f449,f448,f452,f455,f454,f453,f456,f457,f458,f459,f460,f461,f462,f463,f466,f465,f464,f467,f468,f469,f471,f470,f473,f472,f617,f475,f474,f477,f486,f485,f484,f483,f482,f481,f480,f638,f487,f488,f498,f497,f496,f495,f494,f493,f492,f491,f620,f499,f500,f510,f509,f508,f507,f506,f505,f504,f503,f621,f511,f512,f522,f521,f520,f519,f518,f517,f516,f515,f622,f523,f525,f524,f533,f532,f531,f530,f529,f528,f527,f623,f534,f536,f535,f544,f543,f542,f541,f540,f539,f538,f624,f545,f546,f554,f553,f552,f551,f550,f549,f625,f555,f626,f643,f556,f627,f644,f558,f628,f645,f560,f562,f563,f564,f565,f566,f567,f629,f570,f569,f568,f572,f573,f574,f575,f576,f577,f578,f580,f637,f631,f582,f581,f632,f586,f585,f584,f633,f589,f588,f636]) ).
fof(f642,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f609]) ).
fof(f609,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f417]) ).
fof(f417,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f258]) ).
fof(f637,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f630]) ).
fof(f630,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f579]) ).
fof(f579,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f358]) ).
fof(f552,plain,
! [X0] :
( ssList(sK62(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f551,plain,
! [X0] :
( ssList(sK61(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f550,plain,
! [X0] :
( ssItem(sK60(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f549,plain,
! [X0] :
( ssItem(sK59(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f542,plain,
! [X0] :
( ssList(sK58(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f541,plain,
! [X0] :
( ssList(sK57(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f540,plain,
! [X0] :
( ssList(sK56(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f539,plain,
! [X0] :
( ssItem(sK55(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f538,plain,
! [X0] :
( ssItem(sK54(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f531,plain,
! [X0] :
( ssList(sK53(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f530,plain,
! [X0] :
( ssList(sK52(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f529,plain,
! [X0] :
( ssList(sK51(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f528,plain,
! [X0] :
( ssItem(sK50(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f527,plain,
! [X0] :
( ssItem(sK49(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f519,plain,
! [X0] :
( ssList(sK48(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f518,plain,
! [X0] :
( ssList(sK47(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f517,plain,
! [X0] :
( ssList(sK46(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f516,plain,
! [X0] :
( ssItem(sK45(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f515,plain,
! [X0] :
( ssItem(sK44(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f507,plain,
! [X0] :
( ssList(sK43(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f506,plain,
! [X0] :
( ssList(sK42(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f505,plain,
! [X0] :
( ssList(sK41(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f504,plain,
! [X0] :
( ssItem(sK40(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f503,plain,
! [X0] :
( ssItem(sK39(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f495,plain,
! [X0] :
( ssList(sK38(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f494,plain,
! [X0] :
( ssList(sK37(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f493,plain,
! [X0] :
( ssList(sK36(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f492,plain,
! [X0] :
( ssItem(sK35(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f491,plain,
! [X0] :
( ssItem(sK34(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f484,plain,
! [X0] :
( ssList(sK33(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f483,plain,
! [X0] :
( ssList(sK32(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f482,plain,
! [X0] :
( ssList(sK31(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f481,plain,
! [X0] :
( ssItem(sK30(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f480,plain,
! [X0] :
( ssItem(sK29(X0))
| sP4(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f461,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f460,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(f459,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f458,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f457,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f456,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f404,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
fof(f403,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0] :
( ssItem(X0)
=> geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
fof(f402,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ssItem(X0)
=> ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
fof(f401,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f650,plain,
( nil != sK18
| nil = sK21 ),
inference(forward_demodulation,[],[f391,f382]) ).
fof(f555,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f175,f249,f248]) ).
fof(f175,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ssList(X0)
=> ( equalelemsP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(X3,cons(X1,cons(X2,X4))) = X0
=> X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
fof(f545,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f173,f246,f245]) ).
fof(f173,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> lt(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
fof(f534,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f171,f243,f242]) ).
fof(f171,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
fof(f523,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f169,f240,f239]) ).
fof(f169,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ssList(X0)
=> ( cyclefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ~ ( leq(X2,X1)
& leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f511,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f167,f237,f236]) ).
fof(f167,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( lt(X2,X1)
| lt(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
fof(f499,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f165,f234,f233]) ).
fof(f165,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f164]) ).
fof(f164,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( leq(X2,X1)
| leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
fof(f487,plain,
! [X0] :
( sP5(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0] :
( sP5(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f163,f231,f230]) ).
fof(f163,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ssList(X0)
=> ( duplicatefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> X1 != X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
fof(f645,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f391,f390,f389,f388,f387,f386,f385,f384,f383,f382,f381,f380,f379,f378,f377,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f418,f642,f420,f419,f422,f421,f425,f424,f641,f426,f427,f428,f429,f430,f433,f640,f431,f639,f435,f434,f438,f437,f443,f613,f441,f440,f444,f446,f445,f451,f615,f449,f448,f452,f455,f454,f453,f456,f457,f458,f459,f460,f461,f462,f463,f466,f465,f464,f467,f468,f469,f471,f470,f473,f472,f617,f475,f474,f477,f486,f485,f484,f483,f482,f481,f480,f638,f487,f488,f498,f497,f496,f495,f494,f493,f492,f491,f620,f499,f500,f510,f509,f508,f507,f506,f505,f504,f503,f621,f511,f512,f522,f521,f520,f519,f518,f517,f516,f515,f622,f523,f525,f524,f533,f532,f531,f530,f529,f528,f527,f623,f534,f536,f535,f544,f543,f542,f541,f540,f539,f538,f624,f545,f546,f554,f553,f552,f551,f550,f549,f625,f555,f626,f643,f556,f627,f644,f558,f628]) ).
fof(f644,plain,
segmentP(nil,nil),
inference(global_subsumption,[],[f391,f390,f389,f388,f387,f386,f385,f384,f383,f382,f381,f380,f379,f378,f377,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f418,f642,f420,f419,f422,f421,f425,f424,f641,f426,f427,f428,f429,f430,f433,f640,f431,f639,f435,f434,f438,f437,f443,f613,f441,f440,f444,f446,f445,f451,f615,f449,f448,f452,f455,f454,f453,f456,f457,f458,f459,f460,f461,f462,f463,f466,f465,f464,f467,f468,f469,f471,f470,f473,f472,f617,f475,f474,f477,f486,f485,f484,f483,f482,f481,f480,f638,f487,f488,f498,f497,f496,f495,f494,f493,f492,f491,f620,f499,f500,f510,f509,f508,f507,f506,f505,f504,f503,f621,f511,f512,f522,f521,f520,f519,f518,f517,f516,f515,f622,f523,f525,f524,f533,f532,f531,f530,f529,f528,f527,f623,f534,f536,f535,f544,f543,f542,f541,f540,f539,f538,f624,f545,f546,f554,f553,f552,f551,f550,f549,f625,f555,f626,f643,f556,f627]) ).
fof(f643,plain,
rearsegP(nil,nil),
inference(global_subsumption,[],[f391,f390,f389,f388,f387,f386,f385,f384,f383,f382,f381,f380,f379,f378,f377,f392,f393,f394,f395,f396,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f418,f642,f420,f419,f422,f421,f425,f424,f641,f426,f427,f428,f429,f430,f433,f640,f431,f639,f435,f434,f438,f437,f443,f613,f441,f440,f444,f446,f445,f451,f615,f449,f448,f452,f455,f454,f453,f456,f457,f458,f459,f460,f461,f462,f463,f466,f465,f464,f467,f468,f469,f471,f470,f473,f472,f617,f475,f474,f477,f486,f485,f484,f483,f482,f481,f480,f638,f487,f488,f498,f497,f496,f495,f494,f493,f492,f491,f620,f499,f500,f510,f509,f508,f507,f506,f505,f504,f503,f621,f511,f512,f522,f521,f520,f519,f518,f517,f516,f515,f622,f523,f525,f524,f533,f532,f531,f530,f529,f528,f527,f623,f534,f536,f535,f544,f543,f542,f541,f540,f539,f538,f624,f545,f546,f554,f553,f552,f551,f550,f549,f625,f555,f626]) ).
fof(f615,plain,
! [X1] : sP2(nil,X1),
inference(equality_resolution,[],[f450]) ).
fof(f450,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f613,plain,
! [X1] : sP0(nil,X1),
inference(equality_resolution,[],[f442]) ).
fof(f442,plain,
! [X0,X1] :
( sP0(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f270]) ).
fof(f608,plain,
sK69 != sK70,
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
( sK69 != sK70
& ssItem(sK70)
& ssItem(sK69) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70])],[f2,f375,f374]) ).
fof(f374,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK69 != X1
& ssItem(X1) )
& ssItem(sK69) ) ),
introduced(choice_axiom,[]) ).
fof(f375,plain,
( ? [X1] :
( sK69 != X1
& ssItem(X1) )
=> ( sK69 != sK70
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f390,plain,
~ neq(sK18,nil),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
( ( nil != sK20
| nil = sK21 )
& ~ neq(sK18,nil)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != sK22
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK20)
& sK21 = app(app(sK22,sK20),sK23)
& ssList(sK23)
& ssList(sK22)
& neq(sK19,nil)
& sK18 = sK20
& sK19 = sK21
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22,sK23])],[f100,f256,f255,f254,f253,f252,f251]) ).
fof(f251,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ~ neq(X0,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ~ neq(sK18,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(X1,nil)
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ~ neq(sK18,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(X1,nil)
& sK18 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ~ neq(sK18,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(sK19,nil)
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ~ neq(sK18,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(sK19,nil)
& sK18 = X2
& sK19 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( nil != sK20
| nil = X3 )
& ~ neq(sK18,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK20)
& app(app(X4,sK20),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(sK19,nil)
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
( ? [X3] :
( ( nil != sK20
| nil = X3 )
& ~ neq(sK18,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK20)
& app(app(X4,sK20),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(sK19,nil)
& sK18 = sK20
& sK19 = X3
& ssList(X3) )
=> ( ( nil != sK20
| nil = sK21 )
& ~ neq(sK18,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK20)
& app(app(X4,sK20),X5) = sK21
& ssList(X5) )
& ssList(X4) )
& neq(sK19,nil)
& sK18 = sK20
& sK19 = sK21
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f255,plain,
( ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK20)
& app(app(X4,sK20),X5) = sK21
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != sK22
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK20)
& sK21 = app(app(sK22,sK20),X5)
& ssList(X5) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f256,plain,
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != sK22
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK20)
& sK21 = app(app(sK22,sK20),X5)
& ssList(X5) )
=> ( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != sK22
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK20)
& sK21 = app(app(sK22,sK20),sK23)
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ~ neq(X0,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ~ neq(X0,nil)
& ? [X4] :
( ? [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( app(X8,cons(X6,nil)) != X2
| ~ ssList(X8) )
| app(cons(X6,nil),X7) != X5
| ~ ssList(X7) )
| ~ ssItem(X6) )
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(cons(X9,nil),X11) != X2
| ~ ssList(X11) )
| app(X10,cons(X9,nil)) != X4
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(app(X4,X2),X5) = X3
& ssList(X5) )
& ssList(X4) )
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X2
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ? [X9] :
( ? [X10] :
( ? [X11] :
( app(cons(X9,nil),X11) = X2
& ssList(X11) )
& app(X10,cons(X9,nil)) = X4
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X5
& ssList(X10) )
& ssItem(X9) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( app(cons(X6,nil),X8) = X2
& ssList(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X5
& ssList(X10) )
& ssItem(X9) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( app(cons(X6,nil),X8) = X2
& ssList(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f383,plain,
neq(sK19,nil),
inference(cnf_transformation,[],[f257]) ).
fof(f648,plain,
equalelemsP(sK18),
inference(superposition,[],[f387,f382]) ).
fof(f382,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f257]) ).
fof(f381,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f257]) ).
fof(f607,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f376]) ).
fof(f606,plain,
ssItem(sK69),
inference(cnf_transformation,[],[f376]) ).
fof(f400,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f399,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(f398,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f397,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
fof(f396,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
fof(f395,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
fof(f394,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f393,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f392,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f387,plain,
equalelemsP(sK20),
inference(cnf_transformation,[],[f257]) ).
fof(f385,plain,
ssList(sK23),
inference(cnf_transformation,[],[f257]) ).
fof(f384,plain,
ssList(sK22),
inference(cnf_transformation,[],[f257]) ).
fof(f380,plain,
ssList(sK21),
inference(cnf_transformation,[],[f257]) ).
fof(f379,plain,
ssList(sK20),
inference(cnf_transformation,[],[f257]) ).
fof(f378,plain,
ssList(sK19),
inference(cnf_transformation,[],[f257]) ).
fof(f377,plain,
ssList(sK18),
inference(cnf_transformation,[],[f257]) ).
fof(f605,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
fof(f604,plain,
! [X2,X0,X1] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
fof(f603,plain,
! [X2,X0,X1] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X0,X1) )
=> rearsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(f602,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f601,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).
fof(f600,plain,
! [X2,X0,X1] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).
fof(f599,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
fof(f598,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X0,X1)
=> rearsegP(app(X2,X0),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(f597,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f595,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f205]) ).
fof(f205,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( X0 = X1
& X2 = X3 )
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3) )
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssItem(X3)
=> ( cons(X2,X0) = cons(X3,X1)
=> ( X0 = X1
& X2 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
fof(f596,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f594,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
fof(f591,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f592,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f636,plain,
( nil = app(nil,nil)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f635]) ).
fof(f635,plain,
( nil = app(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f634]) ).
fof(f634,plain,
! [X1] :
( nil = app(nil,X1)
| nil != X1
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f593]) ).
fof(f593,plain,
! [X0,X1] :
( nil = app(X0,X1)
| nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f588,plain,
! [X0,X1] :
( ssList(sK68(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f371,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f369,f370]) ).
fof(f370,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f368]) ).
fof(f368,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f589,plain,
! [X0,X1] :
( app(X1,sK68(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f633,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f590]) ).
fof(f590,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f584,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f367,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
& ssList(sK67(X0,X1))
& ssList(sK66(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67])],[f364,f366,f365]) ).
fof(f365,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK66(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f366,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK66(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f364,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f363]) ).
fof(f363,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f585,plain,
! [X0,X1] :
( ssList(sK67(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f586,plain,
! [X0,X1] :
( app(app(sK66(X0,X1),X1),sK67(X0,X1)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f632,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f587]) ).
fof(f587,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f581,plain,
! [X0,X1] :
( ssList(sK65(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f362,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f360,f361]) ).
fof(f361,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK65(X0,X1),X1) = X0
& ssList(sK65(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f360,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f359]) ).
fof(f359,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f582,plain,
! [X0,X1] :
( app(sK65(X0,X1),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f631,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f583]) ).
fof(f583,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f578,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f577,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f576,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f575,plain,
! [X0,X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f191]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| tl(X0) != tl(X1)
| hd(X0) != hd(X1)
| nil = X0
| nil = X1
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( tl(X0) = tl(X1)
& hd(X0) = hd(X1)
& nil != X0
& nil != X1 )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax77) ).
fof(f574,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
fof(f573,plain,
! [X0,X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
fof(f568,plain,
! [X0,X1] :
( ssList(sK63(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1))
& ssList(sK63(X0,X1)) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f354,f356,f355]) ).
fof(f355,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
& ssList(sK63(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
! [X0,X1] :
( ? [X5] :
( app(sK63(X0,X1),cons(X1,X5)) = X0
& ssList(X5) )
=> ( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
& ssList(sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f353]) ).
fof(f353,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f185]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f569,plain,
! [X0,X1] :
( ssList(sK64(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f570,plain,
! [X0,X1] :
( app(sK63(X0,X1),cons(X1,sK64(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f629,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f571]) ).
fof(f571,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f567,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f628,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f561]) ).
fof(f561,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f627,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f559]) ).
fof(f559,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f626,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f557]) ).
fof(f557,plain,
! [X0] :
( rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f350]) ).
fof(f625,plain,
! [X8,X6,X7,X5] :
( X5 = X6
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP16(app(X7,cons(X5,cons(X6,X8)))) ),
inference(equality_resolution,[],[f548]) ).
fof(f548,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f553,plain,
! [X0] :
( sP16(X0)
| app(sK61(X0),cons(sK59(X0),cons(sK60(X0),sK62(X0)))) = X0 ),
inference(cnf_transformation,[],[f349]) ).
fof(f624,plain,
! [X10,X8,X6,X9,X7] :
( lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f537]) ).
fof(f537,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f341]) ).
fof(f543,plain,
! [X0] :
( sP14(X0)
| app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0 ),
inference(cnf_transformation,[],[f341]) ).
fof(f623,plain,
! [X10,X8,X6,X9,X7] :
( leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f526]) ).
fof(f526,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f332]) ).
fof(f532,plain,
! [X0] :
( sP12(X0)
| app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0 ),
inference(cnf_transformation,[],[f332]) ).
fof(f622,plain,
! [X10,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f514]) ).
fof(f514,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f520,plain,
! [X0] :
( sP10(X0)
| app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0 ),
inference(cnf_transformation,[],[f323]) ).
fof(f621,plain,
! [X10,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f502]) ).
fof(f502,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f314]) ).
fof(f508,plain,
! [X0] :
( sP8(X0)
| app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0 ),
inference(cnf_transformation,[],[f314]) ).
fof(f620,plain,
! [X10,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP6(app(app(X8,cons(X6,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f490]) ).
fof(f490,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f496,plain,
! [X0] :
( sP6(X0)
| app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0 ),
inference(cnf_transformation,[],[f305]) ).
fof(f638,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ sP4(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(duplicate_literal_removal,[],[f619]) ).
fof(f619,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP4(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f618]) ).
fof(f618,plain,
! [X10,X0,X8,X9,X7] :
( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP4(X0) ),
inference(equality_resolution,[],[f479]) ).
fof(f479,plain,
! [X10,X0,X8,X6,X9,X7] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f296]) ).
fof(f485,plain,
! [X0] :
( sP4(X0)
| app(app(sK31(X0),cons(sK29(X0),sK32(X0))),cons(sK30(X0),sK33(X0))) = X0 ),
inference(cnf_transformation,[],[f296]) ).
fof(f617,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f476]) ).
fof(f476,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f469,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f466,plain,
! [X0] :
( cons(sK25(X0),sK24(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f453,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f275]) ).
fof(f275,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f454,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f455,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f451,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f443,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f270]) ).
fof(f434,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f265]) ).
fof(f265,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).
fof(f435,plain,
! [X2,X3,X0,X1] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f639,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f612]) ).
fof(f612,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f436]) ).
fof(f436,plain,
! [X2,X3,X0,X1] :
( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f431,plain,
! [X2,X0,X1] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f433,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f430,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& lt(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
fof(f429,plain,
! [X2,X0,X1] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& leq(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91) ).
fof(f428,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
fof(f427,plain,
! [X2,X0,X1] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X0,X1) )
=> geq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).
fof(f426,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).
fof(f641,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f610]) ).
fof(f610,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f423]) ).
fof(f423,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f425,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f416,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( leq(X1,X0)
& leq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
fof(f415,plain,
! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( geq(X1,X0)
& geq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).
fof(f413,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( leq(X0,X1)
=> ( lt(X0,X1)
| X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).
fof(f386,plain,
sK21 = app(app(sK22,sK20),sK23),
inference(cnf_transformation,[],[f257]) ).
fof(f388,plain,
! [X10,X11,X9] :
( app(cons(X9,nil),X11) != sK20
| ~ ssList(X11)
| app(X10,cons(X9,nil)) != sK22
| ~ ssList(X10)
| ~ ssItem(X9) ),
inference(cnf_transformation,[],[f257]) ).
fof(f389,plain,
! [X8,X6,X7] :
( app(X8,cons(X6,nil)) != sK20
| ~ ssList(X8)
| app(cons(X6,nil),X7) != sK23
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f257]) ).
fof(f391,plain,
( nil != sK20
| nil = sK21 ),
inference(cnf_transformation,[],[f257]) ).
fof(f1123,plain,
( ~ spl71_1
| ~ spl71_2 ),
inference(avatar_contradiction_clause,[],[f1122]) ).
fof(f1122,plain,
( $false
| ~ spl71_1
| ~ spl71_2 ),
inference(global_subsumption,[],[f391,f389,f388,f386,f413,f415,f416,f425,f641,f426,f427,f428,f429,f430,f433,f431,f639,f435,f434,f443,f451,f455,f454,f453,f466,f469,f617,f485,f638,f496,f620,f508,f621,f520,f622,f532,f623,f543,f624,f553,f625,f626,f627,f628,f567,f629,f570,f569,f568,f573,f574,f575,f576,f577,f578,f631,f582,f581,f632,f586,f585,f584,f633,f589,f588,f636,f592,f591,f594,f596,f595,f597,f598,f599,f600,f601,f602,f603,f604,f605,f377,f378,f379,f380,f384,f385,f387,f392,f393,f394,f395,f396,f397,f398,f399,f400,f606,f607,f381,f382,f648,f383,f390,f608,f613,f615,f643,f644,f645,f487,f499,f511,f523,f534,f545,f555,f650,f401,f402,f403,f404,f456,f457,f458,f459,f460,f461,f480,f481,f482,f483,f484,f491,f492,f493,f494,f495,f503,f504,f505,f506,f507,f515,f516,f517,f518,f519,f527,f528,f529,f530,f531,f538,f539,f540,f541,f542,f549,f550,f551,f552,f637,f642,f646,f662,f405,f406,f407,f408,f409,f410,f411,f477,f488,f500,f512,f524,f525,f535,f536,f546,f663,f664,f444,f665,f666,f667,f668,f669,f670,f671,f452,f462,f703,f704,f677,f678,f463,f732,f733,f681,f682,f706,f707,f710,f711,f474,f486,f497,f498,f509,f510,f521,f522,f533,f544,f554,f440,f448,f464,f736,f737,f465,f467,f468,f738,f739,f470,f472,f740,f741,f556,f558,f560,f562,f757,f758,f572,f759,f760,f563,f564,f640,f683,f684,f685,f686,f687,f688,f689,f690,f691,f692,f412,f693,f694,f695,f772,f696,f773,f697,f774,f698,f775,f699,f776,f700,f777,f701,f702,f712,f414,f713,f714,f715,f716,f717,f718,f719,f720,f721,f722,f723,f418,f724,f793,f725,f794,f726,f795,f727,f796,f728,f797,f729,f798,f730,f731,f419,f420,f801,f421,f422,f424,f437,f438,f441,f445,f446,f449,f813,f814,f815,f471,f848,f817,f819,f826,f827,f828,f829,f830,f831,f832,f833,f834,f835,f836,f837,f838,f839,f840,f841,f842,f843,f844,f845,f846,f847,f473,f888,f857,f859,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f880,f881,f882,f883,f884,f885,f886,f887,f824,f475,f825,f565,f924,f925,f926,f927,f956,f957,f934,f935,f936,f937,f938,f939,f940,f941,f942,f943,f944,f945,f946,f947,f948,f949,f950,f951,f952,f953,f954,f955,f928,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f969,f970,f971,f972,f973,f974,f975,f976,f977,f566,f980,f981,f982,f983,f984,f985,f1012,f1013,f988,f989,f990,f991,f992,f993,f994,f995,f996,f997,f998,f999,f1000,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f929,f1014,f1015,f1016,f1017,f1018,f1019,f1020,f1021,f1022,f1023,f1024,f1025,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f932,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1048,f1049,f1050,f1051,f1052,f1053,f1054,f1055,f933,f1058,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1072,f1073,f1074,f1075,f1076,f1077,f580,f1090,f861,f1092,f821,f1094,f1095,f1096,f860,f1097,f1098,f1099,f820,f1100,f654,f1102,f657,f1105,f1113,f1111,f1112,f1101,f1115,f1118]) ).
fof(f1121,plain,
( ~ spl71_1
| ~ spl71_2 ),
inference(avatar_contradiction_clause,[],[f1120]) ).
fof(f1120,plain,
( $false
| ~ spl71_1
| ~ spl71_2 ),
inference(global_subsumption,[],[f391,f389,f388,f386,f413,f415,f416,f425,f641,f426,f427,f428,f429,f430,f433,f431,f639,f435,f434,f443,f451,f455,f454,f453,f466,f469,f617,f485,f638,f496,f620,f508,f621,f520,f622,f532,f623,f543,f624,f553,f625,f626,f627,f628,f567,f629,f570,f569,f568,f573,f574,f575,f576,f577,f578,f631,f582,f581,f632,f586,f585,f584,f633,f589,f588,f636,f592,f591,f594,f596,f595,f597,f598,f599,f600,f601,f602,f603,f604,f605,f377,f378,f379,f380,f384,f385,f387,f392,f393,f394,f395,f396,f397,f398,f399,f400,f606,f607,f381,f382,f648,f383,f390,f608,f613,f615,f643,f644,f645,f487,f499,f511,f523,f534,f545,f555,f650,f401,f402,f403,f404,f456,f457,f458,f459,f460,f461,f480,f481,f482,f483,f484,f491,f492,f493,f494,f495,f503,f504,f505,f506,f507,f515,f516,f517,f518,f519,f527,f528,f529,f530,f531,f538,f539,f540,f541,f542,f549,f550,f551,f552,f637,f642,f646,f662,f405,f406,f407,f408,f409,f410,f411,f477,f488,f500,f512,f524,f525,f535,f536,f546,f663,f664,f444,f665,f666,f667,f668,f669,f670,f671,f452,f462,f703,f704,f677,f678,f463,f732,f733,f681,f682,f706,f707,f710,f711,f474,f486,f497,f498,f509,f510,f521,f522,f533,f544,f554,f440,f448,f464,f736,f737,f465,f467,f468,f738,f739,f470,f472,f740,f741,f556,f558,f560,f562,f757,f758,f572,f759,f760,f563,f564,f640,f683,f684,f685,f686,f687,f688,f689,f690,f691,f692,f412,f693,f694,f695,f772,f696,f773,f697,f774,f698,f775,f699,f776,f700,f777,f701,f702,f712,f414,f713,f714,f715,f716,f717,f718,f719,f720,f721,f722,f723,f418,f724,f793,f725,f794,f726,f795,f727,f796,f728,f797,f729,f798,f730,f731,f419,f420,f801,f421,f422,f424,f437,f438,f441,f445,f446,f449,f813,f814,f815,f471,f848,f817,f819,f826,f827,f828,f829,f830,f831,f832,f833,f834,f835,f836,f837,f838,f839,f840,f841,f842,f843,f844,f845,f846,f847,f473,f888,f857,f859,f864,f865,f866,f867,f868,f869,f870,f871,f872,f873,f874,f875,f876,f877,f878,f879,f880,f881,f882,f883,f884,f885,f886,f887,f824,f475,f825,f565,f924,f925,f926,f927,f956,f957,f934,f935,f936,f937,f938,f939,f940,f941,f942,f943,f944,f945,f946,f947,f948,f949,f950,f951,f952,f953,f954,f955,f928,f958,f959,f960,f961,f962,f963,f964,f965,f966,f967,f968,f969,f970,f971,f972,f973,f974,f975,f976,f977,f566,f980,f981,f982,f983,f984,f985,f1012,f1013,f988,f989,f990,f991,f992,f993,f994,f995,f996,f997,f998,f999,f1000,f1001,f1002,f1003,f1004,f1005,f1006,f1007,f1008,f1009,f1010,f1011,f929,f1014,f1015,f1016,f1017,f1018,f1019,f1020,f1021,f1022,f1023,f1024,f1025,f1026,f1027,f1028,f1029,f1030,f1031,f1032,f1033,f932,f1036,f1037,f1038,f1039,f1040,f1041,f1042,f1043,f1044,f1045,f1046,f1047,f1048,f1049,f1050,f1051,f1052,f1053,f1054,f1055,f933,f1058,f1059,f1060,f1061,f1062,f1063,f1064,f1065,f1066,f1067,f1068,f1069,f1070,f1071,f1072,f1073,f1074,f1075,f1076,f1077,f580,f1090,f861,f1092,f821,f1094,f1095,f1096,f860,f1097,f1098,f1099,f820,f1100,f654,f1102,f657,f1105,f1113,f1111,f1112,f1101,f1115]) ).
fof(f1088,plain,
spl71_2,
inference(avatar_contradiction_clause,[],[f1087]) ).
fof(f1087,plain,
( $false
| spl71_2 ),
inference(subsumption_resolution,[],[f1086,f377]) ).
fof(f1086,plain,
( ~ ssList(sK18)
| spl71_2 ),
inference(subsumption_resolution,[],[f1085,f400]) ).
fof(f1085,plain,
( ~ ssList(nil)
| ~ ssList(sK18)
| spl71_2 ),
inference(subsumption_resolution,[],[f1080,f658]) ).
fof(f658,plain,
( nil != sK18
| spl71_2 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f918,plain,
( spl71_7
| spl71_8 ),
inference(avatar_split_clause,[],[f825,f915,f911]) ).
fof(f911,plain,
( spl71_7
<=> hd(sK23) = sK26(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_7])]) ).
fof(f915,plain,
( spl71_8
<=> nil = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_8])]) ).
fof(f908,plain,
( spl71_5
| spl71_6 ),
inference(avatar_split_clause,[],[f824,f905,f901]) ).
fof(f901,plain,
( spl71_5
<=> hd(sK22) = sK26(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_5])]) ).
fof(f905,plain,
( spl71_6
<=> nil = sK22 ),
introduced(avatar_definition,[new_symbols(naming,[spl71_6])]) ).
fof(f792,plain,
( ~ spl71_3
| ~ spl71_4
| spl71_2 ),
inference(avatar_split_clause,[],[f783,f656,f789,f785]) ).
fof(f785,plain,
( spl71_3
<=> ssItem(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_3])]) ).
fof(f789,plain,
( spl71_4
<=> ssItem(nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl71_4])]) ).
fof(f783,plain,
( ~ ssItem(nil)
| ~ ssItem(sK18)
| spl71_2 ),
inference(subsumption_resolution,[],[f778,f658]) ).
fof(f778,plain,
( nil = sK18
| ~ ssItem(nil)
| ~ ssItem(sK18) ),
inference(resolution,[],[f418,f390]) ).
fof(f659,plain,
( spl71_1
| ~ spl71_2 ),
inference(avatar_split_clause,[],[f650,f656,f652]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC213+1 : TPTP v8.2.0. Released v2.4.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n003.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 03:18:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (25663)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (25667)WARNING: value z3 for option sas not known
% 0.15/0.37 % (25667)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37 % (25668)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (25669)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (25670)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (25666)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (25671)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 % (25665)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (25667)First to succeed.
% 0.15/0.39 TRYING [1]
% 0.15/0.40 % (25667)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25663"
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 % (25667)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.41 % (25667)------------------------------
% 0.15/0.41 % (25667)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.41 % (25667)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (25667)Memory used [KB]: 1669
% 0.15/0.41 % (25667)Time elapsed: 0.029 s
% 0.15/0.41 % (25667)Instructions burned: 95 (million)
% 0.15/0.41 % (25663)Success in time 0.05 s
%------------------------------------------------------------------------------