TSTP Solution File: LCL541+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL541+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:47:55 EDT 2024
% Result : Timeout 298.66s 43.05s
% Output : None
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f316388,plain,
$false,
inference(avatar_sat_refutation,[],[f328,f357,f378,f379,f380,f381,f382,f383,f3657,f18107,f97510,f98468,f98469,f98470,f98471,f98472,f98473,f98474,f98475,f98476,f98477,f98478,f98479,f98480,f98481,f98482,f98483,f98484,f98485,f98486,f98487,f98488,f98489,f98490,f98491,f98492,f98493,f98494,f98495,f98496,f98497,f98498,f98499,f98500,f98501,f98502,f98503,f98504,f98505,f98506,f98507,f98508,f98509,f98510,f98511,f98512,f98513,f98514,f98515,f98516,f98517,f98518,f98519,f98520,f98521,f98522,f98523,f98524,f98525,f98526,f98527,f98528,f98529,f98530,f98531,f98532,f98533,f98534,f98535,f98536,f98537,f98538,f98539,f98540,f98541,f98542,f98543,f98544,f98545,f98546,f98547,f98548,f98549,f98550,f98551,f98552,f98553,f98554,f98555,f98556,f98557,f98558,f98559,f98560,f98561,f98562,f98563,f98564,f98565,f98566,f98567,f98568,f98569,f98570,f98571,f98572,f98573,f98574,f98575,f98576,f98577,f98578,f98579,f98580,f98581,f98582,f98583,f98584,f98585,f98586,f98587,f98588,f98589,f98590,f98591,f98592,f98593,f98594,f98595,f98596,f98597,f98598,f98599,f98600,f98601,f98602,f98603,f98604,f98605,f98606,f98607,f98608,f98609,f98610,f98611,f98612,f98613,f98614,f98615,f98616,f98617,f98618,f98619,f98620,f98621,f98622,f98623,f98624,f98625,f98626,f98627,f98628,f98629,f98630,f98631,f98632,f98633,f98634,f98635,f98636,f98637,f98638,f98639,f98640,f98641,f98642,f98643,f98644,f98645,f98646,f98647,f98648,f98649,f98650,f98651,f98652,f98653,f98654,f98655,f98656,f98657,f98658,f98659,f98660,f98661,f98662,f98663,f98664,f98665,f98666,f98667,f98668,f98669,f98670,f98671,f98672,f98673,f98674,f98675,f98676,f98677,f98678,f98679,f98680,f98681,f98682,f98683,f98684,f98685,f98686,f98687,f98688,f98689,f98690,f98691,f98692,f98693,f98694,f98695,f98696,f98697,f98698,f98699,f98700,f98701,f98702,f98703,f98704,f98705,f98706,f98707,f98708,f98709,f98710,f98711,f98712,f98713,f98714,f98715,f98716,f98717,f98718,f98719,f98720,f98721,f98722,f98723,f98724,f98725,f98726,f98727,f98728,f98729,f98730,f98731,f98732,f98733,f98734,f98735,f98736,f98737,f98738,f98739,f98740,f98741,f98742,f98743,f98744,f98745,f98746,f98747,f98748,f98749,f98750,f98751,f98752,f98753,f98754,f98755,f98756,f98757,f98758,f98759,f98760,f98761,f98762,f98763,f98764,f98765,f98766,f98767,f98768,f98769,f98770,f98771,f98772,f98773,f98774,f98775,f98776,f98777,f98778,f98779,f98780,f98781,f98782,f98783,f98784,f98785,f98786,f98787,f98788,f98789,f98790,f98791,f98792,f98793,f98794,f98795,f98796,f98797,f98798,f98799,f98800,f98801,f98802,f98803,f98804,f98805,f98806,f98807,f98808,f98809,f98810,f98811,f98812,f98813,f98814,f98815,f98816,f98817,f98818,f98819,f98820,f98821,f98822,f98823,f98824,f98825,f98826,f98827,f98828,f98829,f98830,f98831,f98832,f98833,f98834,f98835,f98836,f98837,f98838,f98839,f98840,f98841,f98842,f98843,f98844,f98845,f98846,f98847,f98848,f98849,f98850,f98851,f98852,f98853,f98854,f98855,f98856,f98857,f98858,f98859,f98860,f98861,f98862,f98863,f98864,f98865,f98866,f98867,f98868,f98869,f98870,f98871,f98872,f98873,f98874,f98875,f98876,f98877,f98878,f98879,f98880,f98881,f98882,f98883,f98884,f98885,f98886,f98887,f98888,f98889,f98890,f98891,f98892,f98893,f98894,f98895,f98896,f98897,f98898,f98899,f98900,f98901,f98902,f98903,f98904,f98905,f98906,f98907,f98908,f98909,f98910,f98911,f98912,f98913,f98914,f98915,f98916,f98917,f98918,f98919,f98920,f98921,f98922,f98923,f98924,f98925,f98926,f98927,f98928,f98929,f98930,f98931,f98932,f98933,f98934,f98935,f98936,f98937,f98938,f98939,f98940,f98941,f98942,f98943,f98944,f98945,f98946,f98947,f98948,f98949,f98950,f98951,f98952,f98953,f98954,f98955,f98956,f98957,f98958,f98959,f98960,f98961,f98962,f98963,f98964,f98965,f98966,f98967,f98968,f98969,f98970,f98971,f98972,f98973,f98974,f98975,f98976,f98977,f98978,f98979,f98980,f98981,f98982,f98983,f98984,f98985,f98986,f98987,f98988,f98989,f98990,f98991,f98992,f98993,f98994,f98995,f98996,f98997,f98998,f98999,f99000,f99001,f99002,f99003,f99004,f99005,f99006,f99007,f99008,f316350]) ).
fof(f316350,plain,
~ spl2_7,
inference(avatar_contradiction_clause,[],[f316237]) ).
fof(f316237,plain,
( $false
| ~ spl2_7 ),
inference(resolution,[],[f316139,f268]) ).
fof(f268,plain,
~ is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0))),
inference(resolution,[],[f247,f224]) ).
fof(f224,plain,
~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197]) ).
fof(f197,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f137,f159]) ).
fof(f159,plain,
( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
( axiom_m1
| ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
=> axiom_m1 ),
inference(unused_predicate_definition_removal,[],[f63]) ).
fof(f63,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m1) ).
fof(f223,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196]) ).
fof(f196,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f222,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195]) ).
fof(f195,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f221,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194]) ).
fof(f194,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_possibly) ).
fof(f220,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193]) ).
fof(f193,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f219,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192]) ).
fof(f192,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).
fof(f218,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191]) ).
fof(f191,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f190,plain,
op_possibly,
inference(cnf_transformation,[],[f83]) ).
fof(f83,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f189,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f188,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f187,plain,
op_equiv,
inference(cnf_transformation,[],[f87]) ).
fof(f87,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f186,plain,
op_possibly,
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_op_possibly) ).
fof(f185,plain,
op_or,
inference(cnf_transformation,[],[f84]) ).
fof(f84,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f184,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f183,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f182,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f88]) ).
fof(f88,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f181,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f180,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f179,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f178,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f177,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f176,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f175,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f174,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f173,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f172,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f171,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f170,plain,
equivalence_1,
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
equivalence_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f169,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f168,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f167,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f166,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f165,plain,
axiom_K,
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
axiom_K,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_K) ).
fof(f164,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_M) ).
fof(f163,plain,
axiom_4,
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_4) ).
fof(f162,plain,
axiom_B,
inference(cnf_transformation,[],[f82]) ).
fof(f82,axiom,
axiom_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_B) ).
fof(f161,plain,
~ axiom_m1,
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
~ axiom_m1,
inference(flattening,[],[f90]) ).
fof(f90,negated_conjecture,
~ axiom_m1,
inference(negated_conjecture,[],[f89]) ).
fof(f89,conjecture,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f247,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f228,f218]) ).
fof(f228,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201]) ).
fof(f201,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f227,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200]) ).
fof(f200,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,plain,
( axiom_4
=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f56,axiom,
( axiom_4
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f226,plain,
! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199]) ).
fof(f199,plain,
! [X0] :
( is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(ennf_transformation,[],[f107]) ).
fof(f107,plain,
( axiom_B
=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f57,axiom,
( axiom_B
<=> ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_B) ).
fof(f225,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198]) ).
fof(f198,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f316139,plain,
( ! [X2,X1] : is_a_theorem(implies(and(X2,X1),and(X1,X2)))
| ~ spl2_7 ),
inference(superposition,[],[f315796,f303307]) ).
fof(f303307,plain,
( ! [X0,X1] : or(equiv(X0,not(X0)),X1) = X1
| ~ spl2_7 ),
inference(resolution,[],[f303257,f119210]) ).
fof(f119210,plain,
! [X0,X1] :
( ~ is_a_theorem(not(X1))
| or(X1,X0) = X0 ),
inference(subsumption_resolution,[],[f118978,f229]) ).
fof(f229,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202]) ).
fof(f202,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f116]) ).
fof(f116,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_2) ).
fof(f118978,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,or(X1,X0)))
| or(X1,X0) = X0
| ~ is_a_theorem(not(X1)) ),
inference(resolution,[],[f5564,f5808]) ).
fof(f5808,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f5789,f277]) ).
fof(f277,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f222,f219]) ).
fof(f5789,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1711,f252]) ).
fof(f252,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f242,f231]) ).
fof(f231,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204]) ).
fof(f204,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f123]) ).
fof(f123,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
fof(f230,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203]) ).
fof(f203,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
fof(f242,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210,f237,f211,f238,f212,f239,f213,f240,f214,f241,f215]) ).
fof(f215,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f126]) ).
fof(f126,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f241,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210,f237,f211,f238,f212,f239,f213,f240,f214]) ).
fof(f214,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f240,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210,f237,f211,f238,f212,f239,f213]) ).
fof(f213,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).
fof(f239,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210,f237,f211,f238,f212]) ).
fof(f212,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,plain,
( axiom_K
=> ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f54,axiom,
( axiom_K
<=> ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_K) ).
fof(f238,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210,f237,f211]) ).
fof(f211,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f237,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210]) ).
fof(f210,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens) ).
fof(f236,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209]) ).
fof(f209,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,plain,
( equivalence_1
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f13,axiom,
( equivalence_1
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_1) ).
fof(f235,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208]) ).
fof(f208,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_2) ).
fof(f234,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207]) ).
fof(f207,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f233,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206]) ).
fof(f206,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f119]) ).
fof(f119,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
fof(f232,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205]) ).
fof(f205,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f120]) ).
fof(f120,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
fof(f1711,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[],[f721,f358]) ).
fof(f358,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f238,f242]) ).
fof(f721,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f243,f242]) ).
fof(f243,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210,f237,f211,f238,f212,f239,f213,f240,f214,f241,f215,f242,f216]) ).
fof(f216,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f121]) ).
fof(f121,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3) ).
fof(f5564,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| X0 = X1 ),
inference(resolution,[],[f1611,f241]) ).
fof(f1611,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f599,f242]) ).
fof(f599,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f240,f242]) ).
fof(f303257,plain,
( ! [X0] : is_a_theorem(not(equiv(X0,not(X0))))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f303256,f125718]) ).
fof(f125718,plain,
! [X0,X1] : implies(implies(X0,X0),X1) = X1,
inference(resolution,[],[f119168,f727]) ).
fof(f727,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f358,f231]) ).
fof(f119168,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| implies(X1,X0) = X0 ),
inference(subsumption_resolution,[],[f118833,f231]) ).
fof(f118833,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X1,X0)))
| implies(X1,X0) = X0
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f5564,f5789]) ).
fof(f303256,plain,
( ! [X0] : is_a_theorem(implies(implies(not(X0),not(X0)),not(equiv(X0,not(X0)))))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f303255,f119170]) ).
fof(f119170,plain,
! [X0] : implies(X0,X0) = equiv(X0,X0),
inference(subsumption_resolution,[],[f118853,f235]) ).
fof(f118853,plain,
! [X0] :
( ~ is_a_theorem(implies(equiv(X0,X0),implies(X0,X0)))
| implies(X0,X0) = equiv(X0,X0) ),
inference(resolution,[],[f5564,f731]) ).
fof(f731,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f358,f240]) ).
fof(f303255,plain,
( ! [X0] : is_a_theorem(implies(equiv(not(X0),not(X0)),not(equiv(X0,not(X0)))))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f303136,f158721]) ).
fof(f158721,plain,
( ! [X0] : not(X0) = implies(X0,not(X0))
| ~ spl2_7 ),
inference(superposition,[],[f158720,f119146]) ).
fof(f119146,plain,
( ! [X0] : not(not(X0)) = X0
| ~ spl2_7 ),
inference(subsumption_resolution,[],[f119145,f18248]) ).
fof(f18248,plain,
( ! [X0] : is_a_theorem(or(not(X0),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18147,f881]) ).
fof(f881,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f333,f242]) ).
fof(f333,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(not(X0))),or(X0,X1))),
inference(superposition,[],[f316,f277]) ).
fof(f316,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(forward_demodulation,[],[f237,f277]) ).
fof(f18147,plain,
( ! [X0] : is_a_theorem(or(X0,not(not(not(X0)))))
| ~ spl2_7 ),
inference(superposition,[],[f18103,f277]) ).
fof(f18103,plain,
( ! [X1] : is_a_theorem(implies(X1,not(not(X1))))
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f18102]) ).
fof(f18102,plain,
( spl2_7
<=> ! [X1] : is_a_theorem(implies(X1,not(not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f119145,plain,
( ! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| not(not(X0)) = X0 )
| ~ spl2_7 ),
inference(forward_demodulation,[],[f118771,f277]) ).
fof(f118771,plain,
( ! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| not(not(X0)) = X0 )
| ~ spl2_7 ),
inference(resolution,[],[f5564,f18103]) ).
fof(f158720,plain,
( ! [X0] : implies(not(X0),X0) = X0
| ~ spl2_7 ),
inference(forward_demodulation,[],[f119567,f119146]) ).
fof(f119567,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[],[f219,f119158]) ).
fof(f119158,plain,
! [X0] : and(X0,X0) = X0,
inference(subsumption_resolution,[],[f118783,f232]) ).
fof(f118783,plain,
! [X0] :
( ~ is_a_theorem(implies(and(X0,X0),X0))
| and(X0,X0) = X0 ),
inference(resolution,[],[f5564,f728]) ).
fof(f728,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f358,f234]) ).
fof(f303136,plain,
! [X0] : is_a_theorem(implies(equiv(not(X0),implies(X0,not(X0))),not(equiv(X0,not(X0))))),
inference(superposition,[],[f7854,f119158]) ).
fof(f7854,plain,
! [X0,X1] : is_a_theorem(implies(equiv(and(X1,not(X0)),implies(X0,X1)),not(equiv(X0,X1)))),
inference(superposition,[],[f235,f1740]) ).
fof(f1740,plain,
! [X0,X1] : not(equiv(X0,X1)) = implies(implies(X0,X1),and(X1,not(X0))),
inference(superposition,[],[f264,f223]) ).
fof(f264,plain,
! [X2,X0,X1] : implies(X2,and(X0,not(X1))) = not(and(X2,implies(X0,X1))),
inference(superposition,[],[f219,f219]) ).
fof(f315796,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(X0,or(X1,X2)),and(or(X1,X2),X0)))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f12679,f119146]) ).
fof(f12679,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,or(X1,X2)),and(or(X1,X2),not(not(X0))))),
inference(resolution,[],[f2818,f1332]) ).
fof(f1332,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),not(X2)))
| is_a_theorem(implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f329,f282]) ).
fof(f282,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f272,f219]) ).
fof(f272,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f222,f219]) ).
fof(f329,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f316,f242]) ).
fof(f2818,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X1,X2),not(X0)),not(and(X0,or(X1,X2))))),
inference(forward_demodulation,[],[f2817,f277]) ).
fof(f2817,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(not(X1),X2),not(X0)),not(and(X0,or(X1,X2))))),
inference(forward_demodulation,[],[f2751,f282]) ).
fof(f2751,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(and(not(X1),not(X2)),not(X0)),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f316,f279]) ).
fof(f279,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
inference(superposition,[],[f219,f222]) ).
fof(f99008,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97511]) ).
fof(f97511,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f727]) ).
fof(f18106,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f18105]) ).
fof(f18105,plain,
( spl2_8
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f99007,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97515]) ).
fof(f97515,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f231]) ).
fof(f99006,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97516]) ).
fof(f97516,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92525]) ).
fof(f92525,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[],[f10252,f235]) ).
fof(f10252,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(equiv(X2,X2),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f9819,f8133]) ).
fof(f8133,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5923,f242]) ).
fof(f5923,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f1715,f231]) ).
fof(f1715,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f721,f242]) ).
fof(f9819,plain,
! [X0,X1] : is_a_theorem(implies(implies(equiv(X0,X0),X1),X1)),
inference(resolution,[],[f9806,f1711]) ).
fof(f9806,plain,
! [X0,X1] : is_a_theorem(implies(X0,equiv(X1,X1))),
inference(subsumption_resolution,[],[f9700,f727]) ).
fof(f9700,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,equiv(X1,X1)))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(resolution,[],[f8133,f731]) ).
fof(f99005,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97522]) ).
fof(f97522,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92535]) ).
fof(f92535,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,equiv(X2,X2)))),
inference(resolution,[],[f10252,f231]) ).
fof(f99004,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97523]) ).
fof(f97523,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f234]) ).
fof(f99003,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97525]) ).
fof(f97525,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20962]) ).
fof(f20962,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(necessarily(not(X0)),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f19295,f329]) ).
fof(f19295,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(X0),X1),X0))
| ~ spl2_7 ),
inference(resolution,[],[f19278,f6084]) ).
fof(f6084,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,necessarily(X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f6083,f277]) ).
fof(f6083,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,necessarily(X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5966,f277]) ).
fof(f5966,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1715,f225]) ).
fof(f19278,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0))
| ~ spl2_7 ),
inference(superposition,[],[f18301,f219]) ).
fof(f18301,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,X1)),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18248,f8263]) ).
fof(f8263,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f8260,f277]) ).
fof(f8260,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5950,f277]) ).
fof(f5950,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1715,f232]) ).
fof(f99002,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97526]) ).
fof(f97526,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24914]) ).
fof(f24914,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(necessarily(necessarily(not(X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f20966,f329]) ).
fof(f20966,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(necessarily(X0)),X1),X0))
| ~ spl2_7 ),
inference(resolution,[],[f19295,f6084]) ).
fof(f99001,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97527]) ).
fof(f97527,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23549]) ).
fof(f23549,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(and(X1,not(X0)),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f19293,f329]) ).
fof(f19293,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,X1),X2),X1))
| ~ spl2_7 ),
inference(resolution,[],[f19278,f8844]) ).
fof(f8844,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X0,X2)) ),
inference(forward_demodulation,[],[f8841,f277]) ).
fof(f8841,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(not(X0),X2)) ),
inference(superposition,[],[f5951,f277]) ).
fof(f5951,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X2,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1715,f233]) ).
fof(f99000,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97528]) ).
fof(f97528,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23569]) ).
fof(f23569,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(and(not(X0),X1),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f19294,f329]) ).
fof(f19294,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,X1),X2),X0))
| ~ spl2_7 ),
inference(resolution,[],[f19278,f8263]) ).
fof(f98999,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97529]) ).
fof(f97529,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9806]) ).
fof(f98998,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97532]) ).
fof(f97532,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18103]) ).
fof(f98997,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97535]) ).
fof(f97535,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f27584]) ).
fof(f27584,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(not(equiv(X1,X1)))))
| ~ spl2_7 ),
inference(resolution,[],[f18629,f294]) ).
fof(f294,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(superposition,[],[f231,f277]) ).
fof(f18629,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(not(equiv(X1,X1)),X0))
| is_a_theorem(X0) )
| ~ spl2_7 ),
inference(resolution,[],[f18123,f1668]) ).
fof(f1668,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f1617,f277]) ).
fof(f1617,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1027,f1276]) ).
fof(f1276,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1163,f402]) ).
fof(f402,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f258,f287]) ).
fof(f287,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X0),X1),
inference(superposition,[],[f218,f277]) ).
fof(f258,plain,
! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f242,f225]) ).
fof(f1163,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1126,f287]) ).
fof(f1126,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f945,f230]) ).
fof(f945,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f818,f247]) ).
fof(f818,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f575,f242]) ).
fof(f575,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f529,f242]) ).
fof(f529,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))),
inference(forward_demodulation,[],[f239,f218]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f942,f242]) ).
fof(f942,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f784,f242]) ).
fof(f784,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(resolution,[],[f244,f358]) ).
fof(f244,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210,f237,f211,f238,f212,f239,f213,f240,f214,f241,f215,f242,f216,f243,f217]) ).
fof(f217,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3) ).
fof(f18123,plain,
( ! [X0] : is_a_theorem(necessarily(not(not(equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f10250]) ).
fof(f10250,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f9819,f5861]) ).
fof(f5861,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5813,f247]) ).
fof(f5813,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f5804,f218]) ).
fof(f5804,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f5789,f945]) ).
fof(f98996,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97536]) ).
fof(f97536,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28251]) ).
fof(f28251,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl2_7 ),
inference(resolution,[],[f18654,f294]) ).
fof(f18654,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(not(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) )
| ~ spl2_7 ),
inference(resolution,[],[f18127,f1668]) ).
fof(f18127,plain,
( ! [X0] : is_a_theorem(necessarily(not(not(strict_equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f10273]) ).
fof(f10273,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(strict_equiv(X1,X1),X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f9831,f5861]) ).
fof(f9831,plain,
! [X0,X1] : is_a_theorem(implies(implies(strict_equiv(X0,X0),X1),X1)),
inference(resolution,[],[f9808,f1711]) ).
fof(f9808,plain,
! [X0,X1] : is_a_theorem(implies(X0,strict_equiv(X1,X1))),
inference(subsumption_resolution,[],[f9790,f1913]) ).
fof(f1913,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f1867,f742]) ).
fof(f742,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[],[f727,f277]) ).
fof(f1867,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1181,f404]) ).
fof(f404,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f228,f287]) ).
fof(f1181,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(forward_demodulation,[],[f1180,f218]) ).
fof(f1180,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(forward_demodulation,[],[f1141,f287]) ).
fof(f1141,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,not(X1))))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f945,f316]) ).
fof(f9790,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,strict_equiv(X1,X1)))
| ~ is_a_theorem(strict_implies(X1,X1)) ),
inference(resolution,[],[f8133,f753]) ).
fof(f753,plain,
! [X0] : is_a_theorem(implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(superposition,[],[f728,f220]) ).
fof(f98995,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97537]) ).
fof(f97537,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19264]) ).
fof(f19264,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(not(X0),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f18301,f329]) ).
fof(f98994,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97538]) ).
fof(f97538,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22736]) ).
fof(f22736,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(X1,necessarily(not(X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f19173,f329]) ).
fof(f19173,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,necessarily(X1))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18300,f6084]) ).
fof(f18300,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,X1)),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18248,f8844]) ).
fof(f98993,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97539]) ).
fof(f97539,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23224]) ).
fof(f23224,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(necessarily(not(X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f19268,f329]) ).
fof(f19268,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(necessarily(X0),X1)),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18301,f6084]) ).
fof(f98992,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97540]) ).
fof(f97540,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20197]) ).
fof(f20197,plain,
( ! [X0] : is_a_theorem(implies(X0,not(necessarily(necessarily(not(X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f18408,f329]) ).
fof(f18408,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(X0))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18302,f6084]) ).
fof(f18302,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(X0)),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18248,f6084]) ).
fof(f98991,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97541]) ).
fof(f97541,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23709]) ).
fof(f23709,plain,
( ! [X0] : is_a_theorem(implies(X0,not(necessarily(necessarily(necessarily(not(X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f20201,f329]) ).
fof(f20201,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(necessarily(X0)))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18408,f6084]) ).
fof(f98990,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97542]) ).
fof(f97542,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22648]) ).
fof(f22648,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(necessarily(and(X1,not(X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f18406,f329]) ).
fof(f18406,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,X1))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18302,f8844]) ).
fof(f98989,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97543]) ).
fof(f97543,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22667]) ).
fof(f22667,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(necessarily(and(not(X0),X1)))))
| ~ spl2_7 ),
inference(resolution,[],[f18407,f329]) ).
fof(f18407,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,X1))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18302,f8263]) ).
fof(f98988,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97544]) ).
fof(f97544,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f728]) ).
fof(f98987,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97547]) ).
fof(f97547,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10400]) ).
fof(f10400,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),X0))),
inference(resolution,[],[f9835,f234]) ).
fof(f9835,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f9821,f1027]) ).
fof(f9821,plain,
! [X0,X1] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[],[f9806,f277]) ).
fof(f98986,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97548]) ).
fof(f97548,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10704]) ).
fof(f10704,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(strict_equiv(X1,X1),X0))),
inference(resolution,[],[f9852,f234]) ).
fof(f9852,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(strict_equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f9833,f1027]) ).
fof(f9833,plain,
! [X0,X1] : is_a_theorem(or(X0,strict_equiv(X1,X1))),
inference(superposition,[],[f9808,f277]) ).
fof(f98985,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97550]) ).
fof(f97550,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f14443]) ).
fof(f14443,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(possibly(equiv(X1,X1)),X0))),
inference(resolution,[],[f11762,f234]) ).
fof(f11762,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f11730,f1027]) ).
fof(f11730,plain,
! [X0,X1] : is_a_theorem(or(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f11701,f6464]) ).
fof(f6464,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f6084,f1196]) ).
fof(f1196,plain,
! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1159,f402]) ).
fof(f1159,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1120,f218]) ).
fof(f1120,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f945,f231]) ).
fof(f11701,plain,
! [X0] : is_a_theorem(necessarily(necessarily(possibly(equiv(X0,X0))))),
inference(resolution,[],[f10250,f226]) ).
fof(f98984,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97551]) ).
fof(f97551,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f14896]) ).
fof(f14896,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(possibly(strict_equiv(X1,X1)),X0))),
inference(resolution,[],[f12144,f234]) ).
fof(f12144,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f12112,f1027]) ).
fof(f12112,plain,
! [X0,X1] : is_a_theorem(or(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12086,f6464]) ).
fof(f12086,plain,
! [X0] : is_a_theorem(necessarily(necessarily(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f10273,f226]) ).
fof(f98983,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97560]) ).
fof(f97560,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11975]) ).
fof(f11975,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),possibly(X0)))),
inference(forward_demodulation,[],[f11956,f221]) ).
fof(f11956,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),not(necessarily(not(X0)))))),
inference(resolution,[],[f10257,f1332]) ).
fof(f10257,plain,
! [X0,X1] : is_a_theorem(implies(implies(equiv(X0,X0),necessarily(X1)),X1)),
inference(resolution,[],[f9819,f5966]) ).
fof(f98982,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97561]) ).
fof(f97561,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12284]) ).
fof(f12284,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(strict_equiv(X1,X1),possibly(X0)))),
inference(forward_demodulation,[],[f12265,f221]) ).
fof(f12265,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(strict_equiv(X1,X1),not(necessarily(not(X0)))))),
inference(resolution,[],[f10280,f1332]) ).
fof(f10280,plain,
! [X0,X1] : is_a_theorem(implies(implies(strict_equiv(X0,X0),necessarily(X1)),X1)),
inference(resolution,[],[f9831,f5966]) ).
fof(f98981,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97562]) ).
fof(f97562,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f229]) ).
fof(f98980,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97567]) ).
fof(f97567,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92580]) ).
fof(f92580,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(X1,equiv(X2,X2)))),
inference(resolution,[],[f10252,f229]) ).
fof(f98979,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97568]) ).
fof(f97568,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92527]) ).
fof(f92527,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,not(X1)))),
inference(resolution,[],[f10252,f289]) ).
fof(f289,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X1,not(X0)),or(X0,X1))),
inference(superposition,[],[f235,f277]) ).
fof(f98978,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97569]) ).
fof(f97569,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f297]) ).
fof(f297,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,and(X1,not(X0))))),
inference(superposition,[],[f234,f277]) ).
fof(f98977,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97570]) ).
fof(f97570,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f230]) ).
fof(f98976,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97571]) ).
fof(f97571,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92586]) ).
fof(f92586,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(equiv(X1,X1),X2))),
inference(resolution,[],[f10252,f230]) ).
fof(f98975,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97572]) ).
fof(f97572,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f226]) ).
fof(f98974,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97576]) ).
fof(f97576,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92587]) ).
fof(f92587,plain,
! [X0,X1] : is_a_theorem(implies(X0,necessarily(possibly(equiv(X1,X1))))),
inference(resolution,[],[f10252,f226]) ).
fof(f98973,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97580]) ).
fof(f97580,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45624]) ).
fof(f45624,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f41539,f3785]) ).
fof(f3785,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1676,f1886]) ).
fof(f1886,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f1870,f228]) ).
fof(f1870,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1181,f1159]) ).
fof(f1676,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1650,f287]) ).
fof(f1650,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(or(X1,not(X0)))) ),
inference(resolution,[],[f1617,f316]) ).
fof(f41539,plain,
( ! [X0,X1] : is_a_theorem(not(not(strict_implies(not(equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(superposition,[],[f32261,f266]) ).
fof(f266,plain,
! [X0,X1] : possibly(and(X0,not(X1))) = not(strict_implies(X0,X1)),
inference(forward_demodulation,[],[f265,f218]) ).
fof(f265,plain,
! [X0,X1] : possibly(and(X0,not(X1))) = not(necessarily(implies(X0,X1))),
inference(superposition,[],[f221,f219]) ).
fof(f32261,plain,
( ! [X0,X1] : is_a_theorem(not(possibly(and(not(equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f23112,f18164]) ).
fof(f18164,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(not(possibly(X0))) )
| ~ spl2_7 ),
inference(superposition,[],[f18108,f221]) ).
fof(f18108,plain,
( ! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) )
| ~ spl2_7 ),
inference(resolution,[],[f18103,f242]) ).
fof(f23112,plain,
( ! [X0,X1] : is_a_theorem(necessarily(not(and(not(equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f19263,f10260]) ).
fof(f10260,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(equiv(X0,X0),X1))
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f10246,f218]) ).
fof(f10246,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(equiv(X0,X0),X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f9819,f945]) ).
fof(f19263,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(not(X0),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f18301,f1867]) ).
fof(f98972,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97581]) ).
fof(f97581,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45654]) ).
fof(f45654,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f41567,f3785]) ).
fof(f41567,plain,
( ! [X0,X1] : is_a_theorem(not(not(strict_implies(not(strict_equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(superposition,[],[f32366,f266]) ).
fof(f32366,plain,
( ! [X0,X1] : is_a_theorem(not(possibly(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f23120,f18164]) ).
fof(f23120,plain,
( ! [X0,X1] : is_a_theorem(necessarily(not(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f19263,f10283]) ).
fof(f10283,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(strict_equiv(X0,X0),X1))
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f10269,f218]) ).
fof(f10269,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(strict_equiv(X0,X0),X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f9831,f945]) ).
fof(f98971,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97584]) ).
fof(f97584,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9808]) ).
fof(f98970,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97585]) ).
fof(f97585,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6057]) ).
fof(f6057,plain,
! [X0] : is_a_theorem(implies(X0,possibly(X0))),
inference(resolution,[],[f5966,f226]) ).
fof(f98969,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97589]) ).
fof(f97589,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11731]) ).
fof(f11731,plain,
! [X0,X1] : is_a_theorem(implies(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f11701,f6060]) ).
fof(f6060,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f5966,f1195]) ).
fof(f1195,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1159,f261]) ).
fof(f261,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f258,f218]) ).
fof(f98968,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97590]) ).
fof(f97590,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12113]) ).
fof(f12113,plain,
! [X0,X1] : is_a_theorem(implies(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12086,f6060]) ).
fof(f98967,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97599]) ).
fof(f97599,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f238]) ).
fof(f98966,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97600]) ).
fof(f97600,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f240]) ).
fof(f98965,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97601]) ).
fof(f97601,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f243]) ).
fof(f98964,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97602]) ).
fof(f97602,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f244]) ).
fof(f98963,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97606]) ).
fof(f97606,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f784]) ).
fof(f98962,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97608]) ).
fof(f97608,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f788]) ).
fof(f788,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X1),implies(or(X0,X1),implies(or(X2,not(X0)),X1)))),
inference(superposition,[],[f244,f277]) ).
fof(f98961,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97610]) ).
fof(f97610,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f723]) ).
fof(f723,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,not(X0)),implies(or(X0,X1),implies(X2,X1)))),
inference(superposition,[],[f243,f277]) ).
fof(f98960,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97611]) ).
fof(f97611,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f601]) ).
fof(f601,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,not(X0)),implies(or(X0,X1),equiv(X1,not(X0))))),
inference(superposition,[],[f240,f277]) ).
fof(f98959,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97612]) ).
fof(f97612,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f731]) ).
fof(f98958,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97614]) ).
fof(f97614,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2738]) ).
fof(f2738,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,not(and(X0,or(X1,X2)))),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f238,f279]) ).
fof(f98957,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97616]) ).
fof(f97616,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2801]) ).
fof(f2801,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(X3,X0),or(and(X0,or(X1,X2)),not(and(X3,or(X1,X2)))))),
inference(forward_demodulation,[],[f2800,f279]) ).
fof(f2800,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(X3,X0),or(and(X0,or(X1,X2)),implies(X3,and(not(X1),not(X2)))))),
inference(forward_demodulation,[],[f2743,f277]) ).
fof(f2743,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(X3,X0),implies(not(and(X0,or(X1,X2))),implies(X3,and(not(X1),not(X2)))))),
inference(superposition,[],[f243,f279]) ).
fof(f98956,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97617]) ).
fof(f97617,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2085]) ).
fof(f2085,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X3)),implies(and(X2,not(X3)),and(X0,not(X1))))),
inference(superposition,[],[f331,f282]) ).
fof(f331,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,X1)),implies(and(X0,not(X1)),X2))),
inference(superposition,[],[f316,f219]) ).
fof(f98955,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97618]) ).
fof(f97618,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1333]) ).
fof(f1333,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X2,and(X0,not(X1))))),
inference(superposition,[],[f316,f282]) ).
fof(f98954,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97619]) ).
fof(f97619,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3051]) ).
fof(f3051,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),or(X2,X3)),implies(and(not(X2),not(X3)),and(X0,not(X1))))),
inference(superposition,[],[f332,f282]) ).
fof(f332,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,X1)),implies(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f316,f222]) ).
fof(f98953,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97620]) ).
fof(f97620,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1348]) ).
fof(f1348,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),possibly(X2)),implies(necessarily(not(X2)),and(X0,not(X1))))),
inference(superposition,[],[f330,f282]) ).
fof(f330,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,possibly(X0)),implies(necessarily(not(X0)),X1))),
inference(superposition,[],[f316,f221]) ).
fof(f98952,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97622]) ).
fof(f97622,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9819]) ).
fof(f98951,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97623]) ).
fof(f97623,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10257]) ).
fof(f98950,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97624]) ).
fof(f97624,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1315]) ).
fof(f1315,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(and(X0,not(X1)),X3),implies(implies(X2,X3),implies(implies(implies(X0,X1),X2),X3)))),
inference(superposition,[],[f244,f282]) ).
fof(f98949,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97625]) ).
fof(f97625,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1953]) ).
fof(f1953,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(and(not(X0),not(X1)),X3),implies(implies(X2,X3),implies(implies(or(X0,X1),X2),X3)))),
inference(superposition,[],[f244,f283]) ).
fof(f283,plain,
! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(forward_demodulation,[],[f273,f219]) ).
fof(f273,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),X2) = not(and(or(X0,X1),not(X2))),
inference(superposition,[],[f222,f222]) ).
fof(f98948,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97627]) ).
fof(f97627,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2798]) ).
fof(f2798,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(and(not(X1),not(X2)),X0),or(and(X0,or(X1,X2)),equiv(and(not(X1),not(X2)),X0)))),
inference(forward_demodulation,[],[f2740,f277]) ).
fof(f2740,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(and(not(X1),not(X2)),X0),implies(not(and(X0,or(X1,X2))),equiv(and(not(X1),not(X2)),X0)))),
inference(superposition,[],[f240,f279]) ).
fof(f98947,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97628]) ).
fof(f97628,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2837]) ).
fof(f2837,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(or(X2,X3),implies(X0,X1)),not(and(and(X0,not(X1)),or(X2,X3))))),
inference(forward_demodulation,[],[f2836,f277]) ).
fof(f2836,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(implies(not(X2),X3),implies(X0,X1)),not(and(and(X0,not(X1)),or(X2,X3))))),
inference(forward_demodulation,[],[f2780,f282]) ).
fof(f2780,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(and(not(X2),not(X3)),implies(X0,X1)),not(and(and(X0,not(X1)),or(X2,X3))))),
inference(superposition,[],[f331,f279]) ).
fof(f98946,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97629]) ).
fof(f97629,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2818]) ).
fof(f98945,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97630]) ).
fof(f97630,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3076]) ).
fof(f3076,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),or(X2,X3)),not(and(and(not(X2),not(X3)),or(X0,X1))))),
inference(forward_demodulation,[],[f3052,f279]) ).
fof(f3052,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),or(X2,X3)),implies(and(not(X2),not(X3)),and(not(X0),not(X1))))),
inference(superposition,[],[f332,f283]) ).
fof(f98944,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97631]) ).
fof(f97631,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2847]) ).
fof(f2847,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X1,X2),possibly(X0)),not(and(necessarily(not(X0)),or(X1,X2))))),
inference(forward_demodulation,[],[f2846,f277]) ).
fof(f2846,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(not(X1),X2),possibly(X0)),not(and(necessarily(not(X0)),or(X1,X2))))),
inference(forward_demodulation,[],[f2787,f282]) ).
fof(f2787,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(and(not(X1),not(X2)),possibly(X0)),not(and(necessarily(not(X0)),or(X1,X2))))),
inference(superposition,[],[f330,f279]) ).
fof(f98943,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97634]) ).
fof(f97634,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f789]) ).
fof(f789,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(necessarily(not(X0)),X2),implies(implies(X1,X2),implies(implies(possibly(X0),X1),X2)))),
inference(superposition,[],[f244,f281]) ).
fof(f281,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(forward_demodulation,[],[f271,f219]) ).
fof(f271,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = not(and(possibly(X0),not(X1))),
inference(superposition,[],[f222,f221]) ).
fof(f98942,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97636]) ).
fof(f97636,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9831]) ).
fof(f98941,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97637]) ).
fof(f97637,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10280]) ).
fof(f98940,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97638]) ).
fof(f97638,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2084]) ).
fof(f2084,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(possibly(X0),implies(X1,X2)),implies(and(X1,not(X2)),necessarily(not(X0))))),
inference(superposition,[],[f331,f281]) ).
fof(f98939,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97639]) ).
fof(f97639,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f666]) ).
fof(f666,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),not(X1)),implies(X1,necessarily(not(X0))))),
inference(superposition,[],[f316,f281]) ).
fof(f98938,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97640]) ).
fof(f97640,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3050]) ).
fof(f3050,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(possibly(X0),or(X1,X2)),implies(and(not(X1),not(X2)),necessarily(not(X0))))),
inference(superposition,[],[f332,f281]) ).
fof(f98937,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97641]) ).
fof(f97641,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f967]) ).
fof(f967,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),possibly(X1)),implies(necessarily(not(X1)),necessarily(not(X0))))),
inference(superposition,[],[f330,f281]) ).
fof(f98936,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97643]) ).
fof(f97643,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11787]) ).
fof(f11787,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(equiv(X0,X0)),X1),X1)),
inference(resolution,[],[f11731,f1711]) ).
fof(f98935,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97644]) ).
fof(f97644,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12169]) ).
fof(f12169,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(strict_equiv(X0,X0)),X1),X1)),
inference(resolution,[],[f12113,f1711]) ).
fof(f98934,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97645]) ).
fof(f97645,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f235]) ).
fof(f98933,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97646]) ).
fof(f97646,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f236]) ).
fof(f98932,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97647]) ).
fof(f97647,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f289]) ).
fof(f98931,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97648]) ).
fof(f97648,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2737]) ).
fof(f2737,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X0,and(not(X1),not(X2))),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f236,f279]) ).
fof(f98930,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97649]) ).
fof(f97649,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f290]) ).
fof(f290,plain,
! [X0,X1] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f236,f277]) ).
fof(f98929,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97650]) ).
fof(f97650,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2736]) ).
fof(f2736,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(and(not(X1),not(X2)),X0),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f235,f279]) ).
fof(f98928,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97651]) ).
fof(f97651,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f232]) ).
fof(f98927,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97652]) ).
fof(f97652,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f233]) ).
fof(f98926,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97655]) ).
fof(f97655,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8326]) ).
fof(f8326,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,equiv(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f8233,f223]) ).
fof(f8233,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,X2)),X1)),
inference(resolution,[],[f5950,f233]) ).
fof(f98925,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97656]) ).
fof(f97656,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8950]) ).
fof(f8950,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,equiv(X0,X1)),implies(X1,X0))),
inference(superposition,[],[f8801,f223]) ).
fof(f8801,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,X2)),X2)),
inference(resolution,[],[f5951,f233]) ).
fof(f98924,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97659]) ).
fof(f97659,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1314]) ).
fof(f1314,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(X1)),implies(implies(X0,X1),X2))),
inference(superposition,[],[f230,f282]) ).
fof(f98923,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97660]) ).
fof(f97660,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f7848]) ).
fof(f7848,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(equiv(X0,X1)))),
inference(superposition,[],[f1314,f1740]) ).
fof(f98922,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97661]) ).
fof(f97661,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f7853]) ).
fof(f7853,plain,
! [X0,X1] : is_a_theorem(implies(and(X1,not(X0)),not(equiv(X0,X1)))),
inference(superposition,[],[f231,f1740]) ).
fof(f98921,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97662]) ).
fof(f97662,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6067]) ).
fof(f6067,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(strict_implies(X0,X1)))),
inference(resolution,[],[f5966,f611]) ).
fof(f611,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),necessarily(not(strict_implies(X0,X1))))),
inference(superposition,[],[f226,f266]) ).
fof(f98920,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97663]) ).
fof(f97663,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18139]) ).
fof(f18139,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(implies(X0,X1))))
| ~ spl2_7 ),
inference(superposition,[],[f18103,f219]) ).
fof(f98919,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97664]) ).
fof(f97664,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f611]) ).
fof(f98918,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97665]) ).
fof(f97665,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28208]) ).
fof(f28208,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(equiv(X1,X1))),X2))
| ~ spl2_7 ),
inference(resolution,[],[f18632,f19293]) ).
fof(f18632,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,not(equiv(X1,X1))))
| is_a_theorem(X0) )
| ~ spl2_7 ),
inference(resolution,[],[f18123,f2962]) ).
fof(f2962,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X1)))
| is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f2946,f1456]) ).
fof(f1456,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1438,f242]) ).
fof(f1438,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1160,f261]) ).
fof(f1160,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,and(X0,X1)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1121,f218]) ).
fof(f1121,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(implies(X1,and(X0,X1)))) ),
inference(resolution,[],[f945,f234]) ).
fof(f2946,plain,
! [X0,X1] :
( ~ is_a_theorem(and(not(X1),or(X0,X1)))
| is_a_theorem(X0) ),
inference(resolution,[],[f2910,f242]) ).
fof(f2910,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),or(X1,X0)),X1)),
inference(resolution,[],[f2795,f329]) ).
fof(f2795,plain,
! [X0,X1] : is_a_theorem(or(X1,not(and(not(X0),or(X1,X0))))),
inference(forward_demodulation,[],[f2726,f277]) ).
fof(f2726,plain,
! [X0,X1] : is_a_theorem(implies(not(X1),not(and(not(X0),or(X1,X0))))),
inference(superposition,[],[f234,f279]) ).
fof(f98917,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97666]) ).
fof(f97666,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28457]) ).
fof(f28457,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(strict_equiv(X1,X1))),X2))
| ~ spl2_7 ),
inference(resolution,[],[f18657,f19293]) ).
fof(f18657,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,not(strict_equiv(X1,X1))))
| is_a_theorem(X0) )
| ~ spl2_7 ),
inference(resolution,[],[f18127,f2962]) ).
fof(f98916,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97667]) ).
fof(f97667,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8233]) ).
fof(f98915,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97668]) ).
fof(f97668,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8324]) ).
fof(f8324,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(necessarily(X1),X2)),X1)),
inference(resolution,[],[f8233,f5966]) ).
fof(f98914,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97669]) ).
fof(f97669,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8504]) ).
fof(f8504,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(necessarily(necessarily(X1)),X2)),X1)),
inference(resolution,[],[f8324,f5966]) ).
fof(f98913,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97670]) ).
fof(f97670,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8801]) ).
fof(f98912,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97671]) ).
fof(f97671,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8321]) ).
fof(f8321,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(and(X1,X2),X3)),X1)),
inference(resolution,[],[f8233,f5950]) ).
fof(f98911,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97672]) ).
fof(f97672,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8803]) ).
fof(f8803,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(and(X1,X2),X3)),X2)),
inference(resolution,[],[f5951,f8233]) ).
fof(f98910,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97673]) ).
fof(f97673,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8944]) ).
fof(f8944,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(X1,and(X2,X3))),X3)),
inference(resolution,[],[f8801,f5951]) ).
fof(f98909,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97674]) ).
fof(f97674,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8945]) ).
fof(f8945,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(X1,and(X2,X3))),X2)),
inference(resolution,[],[f8801,f5950]) ).
fof(f98908,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97675]) ).
fof(f97675,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8948]) ).
fof(f8948,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,necessarily(X2))),X2)),
inference(resolution,[],[f8801,f5966]) ).
fof(f98907,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97676]) ).
fof(f97676,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9211]) ).
fof(f9211,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,necessarily(necessarily(X2)))),X2)),
inference(resolution,[],[f8948,f5966]) ).
fof(f98906,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97677]) ).
fof(f97677,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6066]) ).
fof(f6066,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(X1)),X1)),
inference(resolution,[],[f5966,f233]) ).
fof(f98905,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97678]) ).
fof(f97678,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f31861]) ).
fof(f31861,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(not(not(X1)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f22735,f1676]) ).
fof(f22735,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(X1,necessarily(not(X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f19173,f1867]) ).
fof(f98904,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97679]) ).
fof(f97679,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8235]) ).
fof(f8235,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,X2))),X1)),
inference(resolution,[],[f5950,f6066]) ).
fof(f98903,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97680]) ).
fof(f97680,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8409]) ).
fof(f8409,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(necessarily(X1),X2))),X1)),
inference(resolution,[],[f8235,f5966]) ).
fof(f98902,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97681]) ).
fof(f97681,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6149]) ).
fof(f6149,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(X1))),X1)),
inference(resolution,[],[f6066,f5966]) ).
fof(f98901,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97682]) ).
fof(f97682,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6222]) ).
fof(f6222,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(necessarily(X1)))),X1)),
inference(resolution,[],[f6149,f5966]) ).
fof(f98900,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97683]) ).
fof(f97683,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50247]) ).
fof(f50247,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6094,f6149]) ).
fof(f6094,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(necessarily(X1))))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f6074,f1715]) ).
fof(f6074,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(X0)),X0)),
inference(resolution,[],[f5966,f225]) ).
fof(f98899,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97684]) ).
fof(f97684,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8236]) ).
fof(f8236,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(and(X1,X2)))),X1)),
inference(resolution,[],[f5950,f6149]) ).
fof(f98898,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97685]) ).
fof(f97685,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8805]) ).
fof(f8805,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,X2))),X2)),
inference(resolution,[],[f5951,f6066]) ).
fof(f98897,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97686]) ).
fof(f97686,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9036]) ).
fof(f9036,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,necessarily(X2)))),X2)),
inference(resolution,[],[f8805,f5966]) ).
fof(f98896,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97687]) ).
fof(f97687,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8806]) ).
fof(f8806,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(and(X1,X2)))),X2)),
inference(resolution,[],[f5951,f6149]) ).
fof(f98895,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97688]) ).
fof(f97688,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6150]) ).
fof(f6150,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,strict_implies(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f6066,f218]) ).
fof(f98894,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97689]) ).
fof(f97689,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8325]) ).
fof(f8325,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,strict_equiv(X0,X1)),strict_implies(X0,X1))),
inference(superposition,[],[f8233,f220]) ).
fof(f98893,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97690]) ).
fof(f97690,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8949]) ).
fof(f8949,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,strict_equiv(X0,X1)),strict_implies(X1,X0))),
inference(superposition,[],[f8801,f220]) ).
fof(f98892,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97691]) ).
fof(f97691,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8309]) ).
fof(f8309,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(equiv(X0,X1),X2),implies(X0,X1))),
inference(superposition,[],[f8232,f223]) ).
fof(f8232,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,X1),X2),X0)),
inference(resolution,[],[f5950,f232]) ).
fof(f98891,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97692]) ).
fof(f97692,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8892]) ).
fof(f8892,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(equiv(X0,X1),X2),implies(X1,X0))),
inference(superposition,[],[f8800,f223]) ).
fof(f8800,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,X1),X2),X1)),
inference(resolution,[],[f5951,f232]) ).
fof(f98890,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97693]) ).
fof(f97693,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2910]) ).
fof(f98889,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97694]) ).
fof(f97694,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6068]) ).
fof(f6068,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),or(necessarily(X1),X0)),X1)),
inference(resolution,[],[f5966,f2910]) ).
fof(f98888,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97697]) ).
fof(f97697,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1952]) ).
fof(f1952,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2))),
inference(superposition,[],[f230,f283]) ).
fof(f98887,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97698]) ).
fof(f97698,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2735]) ).
fof(f2735,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(not(X1),not(X2)),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f231,f279]) ).
fof(f98886,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97699]) ).
fof(f97699,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28209]) ).
fof(f28209,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(not(equiv(X0,X0)),X1),X2))
| ~ spl2_7 ),
inference(resolution,[],[f18632,f19294]) ).
fof(f98885,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97700]) ).
fof(f97700,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23114]) ).
fof(f23114,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(not(X0)),X1),X0))
| ~ spl2_7 ),
inference(resolution,[],[f19263,f1676]) ).
fof(f98884,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97701]) ).
fof(f97701,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24548]) ).
fof(f24548,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(not(necessarily(X0))),X1),X0))
| ~ spl2_7 ),
inference(resolution,[],[f23114,f5966]) ).
fof(f98883,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97702]) ).
fof(f97702,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28458]) ).
fof(f28458,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl2_7 ),
inference(resolution,[],[f18657,f19294]) ).
fof(f98882,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97703]) ).
fof(f97703,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f39270]) ).
fof(f39270,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(possibly(X0)),X1),not(X0)))
| ~ spl2_7 ),
inference(superposition,[],[f24548,f221]) ).
fof(f98881,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97704]) ).
fof(f97704,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8232]) ).
fof(f98880,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97705]) ).
fof(f97705,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8307]) ).
fof(f8307,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(necessarily(X0),X1),X2),X0)),
inference(resolution,[],[f8232,f5966]) ).
fof(f98879,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97706]) ).
fof(f97706,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8489]) ).
fof(f8489,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(necessarily(necessarily(X0)),X1),X2),X0)),
inference(resolution,[],[f8307,f5966]) ).
fof(f98878,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97707]) ).
fof(f97707,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8800]) ).
fof(f98877,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97708]) ).
fof(f97708,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8890]) ).
fof(f8890,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,necessarily(X1)),X2),X1)),
inference(resolution,[],[f8800,f5966]) ).
fof(f98876,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97709]) ).
fof(f97709,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9195]) ).
fof(f9195,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,necessarily(necessarily(X1))),X2),X1)),
inference(resolution,[],[f8890,f5966]) ).
fof(f98875,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97710]) ).
fof(f97710,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8304]) ).
fof(f8304,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(and(X0,X1),X2),X3),X0)),
inference(resolution,[],[f8232,f5950]) ).
fof(f98874,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97711]) ).
fof(f97711,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8810]) ).
fof(f8810,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(and(X0,X1),X2),X3),X1)),
inference(resolution,[],[f5951,f8232]) ).
fof(f98873,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97712]) ).
fof(f97712,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8886]) ).
fof(f8886,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(X0,and(X1,X2)),X3),X2)),
inference(resolution,[],[f8800,f5951]) ).
fof(f98872,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97713]) ).
fof(f97713,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8887]) ).
fof(f8887,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(X0,and(X1,X2)),X3),X1)),
inference(resolution,[],[f8800,f5950]) ).
fof(f98871,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97714]) ).
fof(f97714,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6065]) ).
fof(f6065,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(X0),X1),X0)),
inference(resolution,[],[f5966,f232]) ).
fof(f98870,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97715]) ).
fof(f97715,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6138]) ).
fof(f6138,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(X0)),X1),X0)),
inference(resolution,[],[f6065,f5966]) ).
fof(f98869,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97716]) ).
fof(f97716,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6211]) ).
fof(f6211,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(necessarily(X0))),X1),X0)),
inference(resolution,[],[f6138,f5966]) ).
fof(f98868,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97717]) ).
fof(f97717,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50263]) ).
fof(f50263,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(necessarily(necessarily(X0)))),X1),X0)),
inference(resolution,[],[f6094,f6138]) ).
fof(f98867,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97718]) ).
fof(f97718,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f32581]) ).
fof(f32581,plain,
( ! [X0,X1] : is_a_theorem(implies(and(necessarily(not(not(X0))),X1),X0))
| ~ spl2_7 ),
inference(resolution,[],[f23223,f1676]) ).
fof(f23223,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(necessarily(not(X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f19268,f1867]) ).
fof(f98866,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97719]) ).
fof(f97719,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8239]) ).
fof(f8239,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,X1)),X2),X0)),
inference(resolution,[],[f5950,f6065]) ).
fof(f98865,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97720]) ).
fof(f97720,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8426]) ).
fof(f8426,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(necessarily(X0),X1)),X2),X0)),
inference(resolution,[],[f8239,f5966]) ).
fof(f98864,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97721]) ).
fof(f97721,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8240]) ).
fof(f8240,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(and(X0,X1))),X2),X0)),
inference(resolution,[],[f5950,f6138]) ).
fof(f98863,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97722]) ).
fof(f97722,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8812]) ).
fof(f8812,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,X1)),X2),X1)),
inference(resolution,[],[f5951,f6065]) ).
fof(f98862,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97723]) ).
fof(f97723,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9054]) ).
fof(f9054,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,necessarily(X1))),X2),X1)),
inference(resolution,[],[f8812,f5966]) ).
fof(f98861,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97724]) ).
fof(f97724,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8813]) ).
fof(f8813,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(and(X0,X1))),X2),X1)),
inference(resolution,[],[f5951,f6138]) ).
fof(f98860,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97725]) ).
fof(f97725,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6139]) ).
fof(f6139,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(strict_implies(X0,X1),X2),implies(X0,X1))),
inference(superposition,[],[f6065,f218]) ).
fof(f98859,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97726]) ).
fof(f97726,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8308]) ).
fof(f8308,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(strict_equiv(X0,X1),X2),strict_implies(X0,X1))),
inference(superposition,[],[f8232,f220]) ).
fof(f98858,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97727]) ).
fof(f97727,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8891]) ).
fof(f8891,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(strict_equiv(X0,X1),X2),strict_implies(X1,X0))),
inference(superposition,[],[f8800,f220]) ).
fof(f98857,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97735]) ).
fof(f97735,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f725]) ).
fof(f725,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))),
inference(forward_demodulation,[],[f722,f277]) ).
fof(f722,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X0),X2)))),
inference(superposition,[],[f243,f277]) ).
fof(f98856,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97736]) ).
fof(f97736,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f600]) ).
fof(f600,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,not(X0)),equiv(not(X0),X1)))),
inference(superposition,[],[f240,f277]) ).
fof(f98855,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97737]) ).
fof(f97737,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f787]) ).
fof(f787,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X2,X1),implies(or(not(X0),X2),X1)))),
inference(superposition,[],[f244,f277]) ).
fof(f98854,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97741]) ).
fof(f97741,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f331]) ).
fof(f98853,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97742]) ).
fof(f97742,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f849]) ).
fof(f849,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,necessarily(not(X1)))),implies(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f316,f263]) ).
fof(f263,plain,
! [X0,X1] : implies(X1,necessarily(not(X0))) = not(and(X1,possibly(X0))),
inference(superposition,[],[f219,f221]) ).
fof(f98852,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97743]) ).
fof(f97743,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1768]) ).
fof(f1768,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,implies(X0,and(X1,not(X2)))),implies(and(X0,implies(X1,X2)),X3))),
inference(superposition,[],[f316,f264]) ).
fof(f98851,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97744]) ).
fof(f97744,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2090]) ).
fof(f2090,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X2,implies(X3,and(X0,possibly(X1)))),implies(and(X3,implies(X0,necessarily(not(X1)))),X2))),
inference(superposition,[],[f331,f263]) ).
fof(f98850,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97745]) ).
fof(f97745,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2092]) ).
fof(f2092,plain,
! [X2,X3,X0,X1,X4] : is_a_theorem(implies(or(X3,implies(X4,and(X0,implies(X1,X2)))),implies(and(X4,implies(X0,and(X1,not(X2)))),X3))),
inference(superposition,[],[f331,f264]) ).
fof(f98849,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97746]) ).
fof(f97746,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2091]) ).
fof(f2091,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X2,implies(X3,and(not(X0),possibly(X1)))),implies(and(X3,or(X0,necessarily(not(X1)))),X2))),
inference(superposition,[],[f331,f274]) ).
fof(f274,plain,
! [X0,X1] : or(X1,necessarily(not(X0))) = not(and(not(X1),possibly(X0))),
inference(superposition,[],[f222,f221]) ).
fof(f98848,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97747]) ).
fof(f97747,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2471]) ).
fof(f2471,plain,
! [X2,X3,X0,X1,X4] : is_a_theorem(implies(or(X3,implies(X4,and(not(X0),implies(X1,X2)))),implies(and(X4,or(X0,and(X1,not(X2)))),X3))),
inference(superposition,[],[f331,f275]) ).
fof(f275,plain,
! [X2,X0,X1] : or(X2,and(X0,not(X1))) = not(and(not(X2),implies(X0,X1))),
inference(superposition,[],[f222,f219]) ).
fof(f98847,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97748]) ).
fof(f97748,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f316]) ).
fof(f98846,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97749]) ).
fof(f97749,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f333]) ).
fof(f98845,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97750]) ).
fof(f97750,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f783]) ).
fof(f783,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),equiv(not(X0),not(X0)))),
inference(superposition,[],[f731,f277]) ).
fof(f98844,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97751]) ).
fof(f97751,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f361]) ).
fof(f361,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[],[f359,f277]) ).
fof(f359,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,implies(not(X0),X1)),implies(not(X0),X1))),
inference(superposition,[],[f238,f277]) ).
fof(f98843,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97752]) ).
fof(f97752,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f332]) ).
fof(f98842,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97753]) ).
fof(f97753,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1062]) ).
fof(f1062,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,necessarily(not(X1)))),implies(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f316,f274]) ).
fof(f98841,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97754]) ).
fof(f97754,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2468]) ).
fof(f2468,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,or(X0,and(X1,not(X2)))),implies(and(not(X0),implies(X1,X2)),X3))),
inference(superposition,[],[f316,f275]) ).
fof(f98840,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97755]) ).
fof(f97755,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3062]) ).
fof(f3062,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X2,or(X3,and(not(X0),not(X1)))),implies(and(not(X3),or(X0,X1)),X2))),
inference(superposition,[],[f332,f222]) ).
fof(f98839,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97756]) ).
fof(f97756,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3063]) ).
fof(f3063,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X2,or(X3,and(X0,possibly(X1)))),implies(and(not(X3),implies(X0,necessarily(not(X1)))),X2))),
inference(superposition,[],[f332,f263]) ).
fof(f98838,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97757]) ).
fof(f97757,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3064]) ).
fof(f3064,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X2,or(X3,and(not(X0),possibly(X1)))),implies(and(not(X3),or(X0,necessarily(not(X1)))),X2))),
inference(superposition,[],[f332,f274]) ).
fof(f98837,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97758]) ).
fof(f97758,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3065]) ).
fof(f3065,plain,
! [X2,X3,X0,X1,X4] : is_a_theorem(implies(or(X3,or(X4,and(X0,implies(X1,X2)))),implies(and(not(X4),implies(X0,and(X1,not(X2)))),X3))),
inference(superposition,[],[f332,f264]) ).
fof(f98836,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97759]) ).
fof(f97759,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3056]) ).
fof(f3056,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X2,or(and(X0,possibly(X1)),X3)),implies(and(implies(X0,necessarily(not(X1))),not(X3)),X2))),
inference(superposition,[],[f332,f263]) ).
fof(f98835,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97760]) ).
fof(f97760,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3058]) ).
fof(f3058,plain,
! [X2,X3,X0,X1,X4] : is_a_theorem(implies(or(X3,or(and(X0,implies(X1,X2)),X4)),implies(and(implies(X0,and(X1,not(X2))),not(X4)),X3))),
inference(superposition,[],[f332,f264]) ).
fof(f98834,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97762]) ).
fof(f97762,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f330]) ).
fof(f98833,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97763]) ).
fof(f97763,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f980]) ).
fof(f980,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,possibly(and(X0,possibly(X1)))),implies(strict_implies(X0,necessarily(not(X1))),X2))),
inference(forward_demodulation,[],[f971,f218]) ).
fof(f971,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,possibly(and(X0,possibly(X1)))),implies(necessarily(implies(X0,necessarily(not(X1)))),X2))),
inference(superposition,[],[f330,f263]) ).
fof(f98832,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97764]) ).
fof(f97764,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1818]) ).
fof(f1818,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,possibly(and(X0,implies(X1,X2)))),implies(strict_implies(X0,and(X1,not(X2))),X3))),
inference(forward_demodulation,[],[f1770,f218]) ).
fof(f1770,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,possibly(and(X0,implies(X1,X2)))),implies(necessarily(implies(X0,and(X1,not(X2)))),X3))),
inference(superposition,[],[f330,f264]) ).
fof(f98831,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97765]) ).
fof(f97765,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f3423]) ).
fof(f3423,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,possibly(and(not(X0),or(X1,X2)))),implies(strict_implies(not(X0),and(not(X1),not(X2))),X3))),
inference(forward_demodulation,[],[f3332,f287]) ).
fof(f3332,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,possibly(and(not(X0),or(X1,X2)))),implies(necessarily(or(X0,and(not(X1),not(X2)))),X3))),
inference(superposition,[],[f330,f276]) ).
fof(f276,plain,
! [X2,X0,X1] : or(X2,and(not(X0),not(X1))) = not(and(not(X2),or(X0,X1))),
inference(superposition,[],[f222,f222]) ).
fof(f98830,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97767]) ).
fof(f97767,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28077]) ).
fof(f28077,plain,
( ! [X0,X1] : is_a_theorem(implies(or(not(equiv(X0,X0)),X1),X1))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f28058,f277]) ).
fof(f28058,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(not(equiv(X0,X0))),X1),X1))
| ~ spl2_7 ),
inference(resolution,[],[f27584,f1711]) ).
fof(f98829,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97768]) ).
fof(f97768,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28323]) ).
fof(f28323,plain,
( ! [X0,X1] : is_a_theorem(implies(or(not(strict_equiv(X0,X0)),X1),X1))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f28304,f277]) ).
fof(f28304,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(not(strict_equiv(X0,X0))),X1),X1))
| ~ spl2_7 ),
inference(resolution,[],[f28251,f1711]) ).
fof(f98828,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97769]) ).
fof(f97769,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f225]) ).
fof(f98827,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97774]) ).
fof(f97774,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f227]) ).
fof(f98826,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97777]) ).
fof(f97777,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8277]) ).
fof(f8277,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f8246,f223]) ).
fof(f8246,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,X1)),X0)),
inference(resolution,[],[f5950,f225]) ).
fof(f98825,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97778]) ).
fof(f97778,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8859]) ).
fof(f8859,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,X1)),implies(X1,X0))),
inference(superposition,[],[f8820,f223]) ).
fof(f8820,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,X1)),X1)),
inference(resolution,[],[f5951,f225]) ).
fof(f98824,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97779]) ).
fof(f97779,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8279]) ).
fof(f8279,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(not(X0),X1)),or(X0,X1))),
inference(superposition,[],[f8246,f468]) ).
fof(f468,plain,
! [X0,X1] : equiv(not(X0),X1) = and(or(X0,X1),implies(X1,not(X0))),
inference(superposition,[],[f223,f277]) ).
fof(f98823,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97780]) ).
fof(f97780,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8860]) ).
fof(f8860,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,not(X1))),or(X1,X0))),
inference(superposition,[],[f8820,f469]) ).
fof(f469,plain,
! [X0,X1] : equiv(X1,not(X0)) = and(implies(X1,not(X0)),or(X0,X1)),
inference(superposition,[],[f223,f277]) ).
fof(f98822,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97786]) ).
fof(f97786,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f653]) ).
fof(f653,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(not(X0)),implies(possibly(X0),X1))),
inference(superposition,[],[f230,f281]) ).
fof(f98821,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97787]) ).
fof(f97787,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6075]) ).
fof(f6075,plain,
! [X0] : is_a_theorem(implies(necessarily(not(X0)),not(necessarily(possibly(X0))))),
inference(resolution,[],[f5966,f339]) ).
fof(f339,plain,
! [X0] : is_a_theorem(implies(necessarily(not(X0)),necessarily(not(necessarily(possibly(X0)))))),
inference(superposition,[],[f226,f245]) ).
fof(f245,plain,
! [X0] : possibly(necessarily(not(X0))) = not(necessarily(possibly(X0))),
inference(superposition,[],[f221,f221]) ).
fof(f98820,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97788]) ).
fof(f97788,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18134]) ).
fof(f18134,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(X0)),not(possibly(X0))))
| ~ spl2_7 ),
inference(superposition,[],[f18103,f221]) ).
fof(f98819,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97789]) ).
fof(f97789,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f339]) ).
fof(f98818,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97790]) ).
fof(f97790,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24799]) ).
fof(f24799,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(equiv(X0,X0))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f20961,f10261]) ).
fof(f10261,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f10247,f218]) ).
fof(f10247,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(equiv(X1,X1),X0))) ),
inference(resolution,[],[f9819,f1617]) ).
fof(f20961,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(necessarily(not(X0)),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f19295,f1867]) ).
fof(f98817,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97791]) ).
fof(f97791,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f51019]) ).
fof(f51019,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(not(necessarily(X0)))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f6422,f18250]) ).
fof(f18250,plain,
( ! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18147,f1867]) ).
fof(f6422,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,necessarily(X1)))
| is_a_theorem(implies(necessarily(X0),X1)) ),
inference(resolution,[],[f6073,f5966]) ).
fof(f6073,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f5966,f575]) ).
fof(f98816,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97792]) ).
fof(f97792,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f51090]) ).
fof(f51090,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(not(necessarily(necessarily(X0))))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f51019,f5966]) ).
fof(f98815,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97793]) ).
fof(f97793,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24805]) ).
fof(f24805,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(strict_equiv(X0,X0))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f20961,f10284]) ).
fof(f10284,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(strict_equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f10270,f218]) ).
fof(f10270,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(strict_equiv(X1,X1),X0))) ),
inference(resolution,[],[f9831,f1617]) ).
fof(f98814,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97795]) ).
fof(f97795,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24807]) ).
fof(f24807,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(possibly(equiv(X0,X0)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f20961,f14885]) ).
fof(f14885,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f14870,f218]) ).
fof(f14870,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(possibly(equiv(X1,X1)),X0))) ),
inference(resolution,[],[f11787,f1617]) ).
fof(f98813,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97796]) ).
fof(f97796,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24808]) ).
fof(f24808,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(possibly(strict_equiv(X0,X0)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f20961,f15012]) ).
fof(f15012,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f14997,f218]) ).
fof(f14997,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(possibly(strict_equiv(X1,X1)),X0))) ),
inference(resolution,[],[f12169,f1617]) ).
fof(f98812,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97797]) ).
fof(f97797,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f51017]) ).
fof(f51017,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(possibly(X0))),not(X0)))
| ~ spl2_7 ),
inference(resolution,[],[f6422,f18332]) ).
fof(f18332,plain,
( ! [X0] : is_a_theorem(strict_implies(not(possibly(X0)),necessarily(not(X0))))
| ~ spl2_7 ),
inference(superposition,[],[f18250,f221]) ).
fof(f98811,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97798]) ).
fof(f97798,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8246]) ).
fof(f98810,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97799]) ).
fof(f97799,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8275]) ).
fof(f8275,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(X0),X1)),X0)),
inference(resolution,[],[f8246,f5966]) ).
fof(f98809,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97800]) ).
fof(f97800,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8358]) ).
fof(f8358,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(necessarily(X0)),X1)),X0)),
inference(resolution,[],[f8275,f5966]) ).
fof(f98808,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97801]) ).
fof(f97801,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50293]) ).
fof(f50293,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(necessarily(necessarily(X0))),X1)),X0)),
inference(resolution,[],[f6094,f8275]) ).
fof(f98807,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97802]) ).
fof(f97802,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f31725]) ).
fof(f31725,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(and(not(not(X0)),X1)),X0))
| ~ spl2_7 ),
inference(resolution,[],[f22666,f1676]) ).
fof(f22666,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(necessarily(and(not(X0),X1)))))
| ~ spl2_7 ),
inference(resolution,[],[f18407,f1867]) ).
fof(f98806,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97803]) ).
fof(f97803,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8272]) ).
fof(f8272,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,X1),X2)),X0)),
inference(resolution,[],[f8246,f5950]) ).
fof(f98805,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97804]) ).
fof(f97804,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8451]) ).
fof(f8451,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(necessarily(X0),X1),X2)),X0)),
inference(resolution,[],[f8272,f5966]) ).
fof(f98804,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97805]) ).
fof(f97805,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8355]) ).
fof(f8355,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(and(X0,X1)),X2)),X0)),
inference(resolution,[],[f8275,f5950]) ).
fof(f98803,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97806]) ).
fof(f97806,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8820]) ).
fof(f98802,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97807]) ).
fof(f97807,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f31546]) ).
fof(f31546,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,not(not(X1)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f22647,f1676]) ).
fof(f22647,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(necessarily(and(X1,not(X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f18406,f1867]) ).
fof(f98801,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97808]) ).
fof(f97808,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8854]) ).
fof(f8854,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,X2))),X1)),
inference(resolution,[],[f8820,f5950]) ).
fof(f98800,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97809]) ).
fof(f97809,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9156]) ).
fof(f9156,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(necessarily(X1),X2))),X1)),
inference(resolution,[],[f8854,f5966]) ).
fof(f98799,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97810]) ).
fof(f97810,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8857]) ).
fof(f8857,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(X1))),X1)),
inference(resolution,[],[f8820,f5966]) ).
fof(f98798,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97811]) ).
fof(f97811,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8984]) ).
fof(f8984,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(necessarily(X1)))),X1)),
inference(resolution,[],[f8857,f5966]) ).
fof(f98797,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97812]) ).
fof(f97812,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50300]) ).
fof(f50300,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6094,f8857]) ).
fof(f98796,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97813]) ).
fof(f97813,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8981]) ).
fof(f8981,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(and(X1,X2)))),X1)),
inference(resolution,[],[f8857,f5950]) ).
fof(f98795,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97814]) ).
fof(f97814,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8824]) ).
fof(f8824,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,X1),X2)),X1)),
inference(resolution,[],[f5951,f8246]) ).
fof(f98794,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97815]) ).
fof(f97815,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9072]) ).
fof(f9072,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,necessarily(X1)),X2)),X1)),
inference(resolution,[],[f8824,f5966]) ).
fof(f98793,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97816]) ).
fof(f97816,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8825]) ).
fof(f8825,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(and(X0,X1)),X2)),X1)),
inference(resolution,[],[f5951,f8275]) ).
fof(f98792,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97817]) ).
fof(f97817,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8853]) ).
fof(f8853,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,X2))),X2)),
inference(resolution,[],[f8820,f5951]) ).
fof(f98791,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97818]) ).
fof(f97818,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9138]) ).
fof(f9138,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,necessarily(X2)))),X2)),
inference(resolution,[],[f8853,f5966]) ).
fof(f98790,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97819]) ).
fof(f97819,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8980]) ).
fof(f8980,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(and(X1,X2)))),X2)),
inference(resolution,[],[f8857,f5951]) ).
fof(f98789,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97820]) ).
fof(f97820,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6074]) ).
fof(f98788,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97821]) ).
fof(f97821,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23603]) ).
fof(f23603,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(not(X0)))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f20196,f1676]) ).
fof(f20196,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(necessarily(not(X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f18408,f1867]) ).
fof(f98787,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97822]) ).
fof(f97822,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24978]) ).
fof(f24978,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(not(necessarily(X0))))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f23603,f5966]) ).
fof(f98786,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97823]) ).
fof(f97823,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8250]) ).
fof(f8250,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,X1))),X0)),
inference(resolution,[],[f5950,f6074]) ).
fof(f98785,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97824]) ).
fof(f97824,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8341]) ).
fof(f8341,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(necessarily(X0),X1))),X0)),
inference(resolution,[],[f8250,f5966]) ).
fof(f98784,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97825]) ).
fof(f97825,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50307]) ).
fof(f50307,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(necessarily(necessarily(X0)),X1))),X0)),
inference(resolution,[],[f6094,f8250]) ).
fof(f98783,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97826]) ).
fof(f97826,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8338]) ).
fof(f8338,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(and(X0,X1),X2))),X0)),
inference(resolution,[],[f8250,f5950]) ).
fof(f98782,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97827]) ).
fof(f97827,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6101]) ).
fof(f6101,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(X0))),X0)),
inference(resolution,[],[f6074,f5966]) ).
fof(f98781,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97828]) ).
fof(f97828,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f38274]) ).
fof(f38274,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(not(not(X0))))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f23708,f1676]) ).
fof(f23708,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(necessarily(necessarily(not(X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f20201,f1867]) ).
fof(f98780,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97829]) ).
fof(f97829,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8251]) ).
fof(f8251,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,X1)))),X0)),
inference(resolution,[],[f5950,f6101]) ).
fof(f98779,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97830]) ).
fof(f97830,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8528]) ).
fof(f8528,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(necessarily(X0),X1)))),X0)),
inference(resolution,[],[f8251,f5966]) ).
fof(f98778,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97831]) ).
fof(f97831,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6160]) ).
fof(f6160,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(X0)))),X0)),
inference(resolution,[],[f6101,f5966]) ).
fof(f98777,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97832]) ).
fof(f97832,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6256]) ).
fof(f6256,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(necessarily(X0))))),X0)),
inference(resolution,[],[f6160,f5966]) ).
fof(f98776,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97833]) ).
fof(f97833,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8252]) ).
fof(f8252,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(and(X0,X1))))),X0)),
inference(resolution,[],[f5950,f6160]) ).
fof(f98775,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97836]) ).
fof(f97836,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28207]) ).
fof(f28207,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(not(equiv(X0,X0)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18632,f20966]) ).
fof(f98774,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97837]) ).
fof(f97837,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28456]) ).
fof(f28456,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(not(strict_equiv(X0,X0)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18657,f20966]) ).
fof(f98773,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97838]) ).
fof(f97838,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8828]) ).
fof(f8828,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,X1))),X1)),
inference(resolution,[],[f5951,f6074]) ).
fof(f98772,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97839]) ).
fof(f97839,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8966]) ).
fof(f8966,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,necessarily(X1)))),X1)),
inference(resolution,[],[f8828,f5966]) ).
fof(f98771,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97840]) ).
fof(f97840,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50318]) ).
fof(f50318,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6094,f8828]) ).
fof(f98770,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97841]) ).
fof(f97841,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8963]) ).
fof(f8963,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,and(X1,X2)))),X1)),
inference(resolution,[],[f8828,f5950]) ).
fof(f98769,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97842]) ).
fof(f97842,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8833]) ).
fof(f8833,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(and(X0,X1),X2))),X1)),
inference(resolution,[],[f5951,f8250]) ).
fof(f98768,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97843]) ).
fof(f97843,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8829]) ).
fof(f8829,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,X1)))),X1)),
inference(resolution,[],[f5951,f6101]) ).
fof(f98767,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97844]) ).
fof(f97844,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9236]) ).
fof(f9236,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,necessarily(X1))))),X1)),
inference(resolution,[],[f8829,f5966]) ).
fof(f98766,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97845]) ).
fof(f97845,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8830]) ).
fof(f8830,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(and(X0,X1))))),X1)),
inference(resolution,[],[f5951,f6160]) ).
fof(f98765,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97846]) ).
fof(f97846,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8962]) ).
fof(f8962,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,and(X1,X2)))),X2)),
inference(resolution,[],[f8828,f5951]) ).
fof(f98764,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97847]) ).
fof(f97847,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6161]) ).
fof(f6161,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(strict_implies(X0,X1))),implies(X0,X1))),
inference(superposition,[],[f6101,f218]) ).
fof(f98763,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97848]) ).
fof(f97848,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8343]) ).
fof(f8343,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(equiv(X0,X1))),implies(X0,X1))),
inference(superposition,[],[f8250,f223]) ).
fof(f98762,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97849]) ).
fof(f97849,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8968]) ).
fof(f8968,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(equiv(X0,X1))),implies(X1,X0))),
inference(superposition,[],[f8828,f223]) ).
fof(f98761,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97850]) ).
fof(f97850,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f42742]) ).
fof(f42742,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(possibly(X0)))),not(X0)))
| ~ spl2_7 ),
inference(superposition,[],[f24978,f221]) ).
fof(f98760,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97851]) ).
fof(f97851,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8342]) ).
fof(f8342,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(strict_equiv(X0,X1))),strict_implies(X0,X1))),
inference(superposition,[],[f8250,f220]) ).
fof(f98759,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97852]) ).
fof(f97852,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8967]) ).
fof(f8967,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(strict_equiv(X0,X1))),strict_implies(X1,X0))),
inference(superposition,[],[f8828,f220]) ).
fof(f98758,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97853]) ).
fof(f97853,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6102]) ).
fof(f6102,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_implies(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f6074,f218]) ).
fof(f98757,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97854]) ).
fof(f97854,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6103]) ).
fof(f6103,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_implies(not(X0),X1)),or(X0,X1))),
inference(superposition,[],[f6074,f287]) ).
fof(f98756,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97855]) ).
fof(f97855,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8276]) ).
fof(f8276,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_equiv(X0,X1)),strict_implies(X0,X1))),
inference(superposition,[],[f8246,f220]) ).
fof(f98755,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97856]) ).
fof(f97856,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f8858]) ).
fof(f8858,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_equiv(X0,X1)),strict_implies(X1,X0))),
inference(superposition,[],[f8820,f220]) ).
fof(f98754,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97858]) ).
fof(f97858,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f753]) ).
fof(f98753,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97859]) ).
fof(f97859,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f248]) ).
fof(f248,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f225,f218]) ).
fof(f98752,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97860]) ).
fof(f97860,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f529]) ).
fof(f98751,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97861]) ).
fof(f97861,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f426]) ).
fof(f426,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(strict_implies(X1,X0),strict_equiv(X0,X1)))),
inference(superposition,[],[f234,f220]) ).
fof(f98750,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97862]) ).
fof(f97862,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f246]) ).
fof(f246,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),necessarily(strict_implies(X0,X1)))),
inference(superposition,[],[f227,f218]) ).
fof(f98749,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97865]) ).
fof(f97865,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f292]) ).
fof(f292,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f248,f277]) ).
fof(f98748,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97866]) ).
fof(f97866,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f576]) ).
fof(f576,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,X1),X2),implies(strict_implies(X0,X1),necessarily(X2)))),
inference(superposition,[],[f529,f218]) ).
fof(f98747,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97867]) ).
fof(f97867,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2216]) ).
fof(f2216,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),implies(strict_implies(not(X0),X1),necessarily(X2)))),
inference(superposition,[],[f576,f277]) ).
fof(f98746,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97868]) ).
fof(f97868,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2760]) ).
fof(f2760,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(not(and(X0,or(X1,X2))),X3),implies(strict_implies(X0,and(not(X1),not(X2))),necessarily(X3)))),
inference(superposition,[],[f576,f279]) ).
fof(f98745,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97869]) ).
fof(f97869,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f578]) ).
fof(f578,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,implies(X0,X1)),implies(necessarily(X2),strict_implies(X0,X1)))),
inference(superposition,[],[f529,f218]) ).
fof(f98744,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97870]) ).
fof(f97870,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2217]) ).
fof(f2217,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(implies(X2,X3),implies(X0,X1)),implies(strict_implies(X2,X3),strict_implies(X0,X1)))),
inference(superposition,[],[f576,f218]) ).
fof(f98743,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97871]) ).
fof(f97871,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2761]) ).
fof(f2761,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(X3,not(and(X0,or(X1,X2)))),implies(necessarily(X3),strict_implies(X0,and(not(X1),not(X2)))))),
inference(superposition,[],[f578,f279]) ).
fof(f98742,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97872]) ).
fof(f97872,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2747]) ).
fof(f2747,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X0,and(not(X1),not(X2))),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f248,f279]) ).
fof(f98741,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97873]) ).
fof(f97873,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2298]) ).
fof(f2298,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,or(X0,X1)),implies(necessarily(X2),strict_implies(not(X0),X1)))),
inference(superposition,[],[f578,f277]) ).
fof(f98740,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97874]) ).
fof(f97874,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f424]) ).
fof(f424,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X0,X1))),
inference(superposition,[],[f232,f220]) ).
fof(f98739,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97875]) ).
fof(f97875,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f425]) ).
fof(f425,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X1,X0))),
inference(superposition,[],[f233,f220]) ).
fof(f98738,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97876]) ).
fof(f97876,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50530]) ).
fof(f50530,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),implies(X0,X1))),
inference(superposition,[],[f6139,f220]) ).
fof(f98737,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97877]) ).
fof(f97877,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50775]) ).
fof(f50775,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),implies(X1,X0))),
inference(superposition,[],[f6150,f220]) ).
fof(f98736,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97878]) ).
fof(f97878,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50560]) ).
fof(f50560,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f50530,f277]) ).
fof(f98735,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97879]) ).
fof(f97879,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f50805]) ).
fof(f50805,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X1,not(X0)),or(X0,X1))),
inference(superposition,[],[f50775,f277]) ).
fof(f98734,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97881]) ).
fof(f97881,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f765]) ).
fof(f765,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(subsumption_resolution,[],[f763,f727]) ).
fof(f763,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[],[f752,f223]) ).
fof(f752,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f728,f242]) ).
fof(f98733,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97892]) ).
fof(f97892,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92680]) ).
fof(f92680,plain,
( ! [X0] : is_a_theorem(not(not(implies(X0,X0))))
| ~ spl2_7 ),
inference(resolution,[],[f92662,f18364]) ).
fof(f18364,plain,
( ! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(not(not(X0))) )
| ~ spl2_7 ),
inference(resolution,[],[f18297,f2180]) ).
fof(f2180,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f1861,f242]) ).
fof(f1861,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1173,f261]) ).
fof(f1173,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(or(X0,X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1172,f218]) ).
fof(f1172,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(implies(or(X0,X0),X1))) ),
inference(forward_demodulation,[],[f1132,f218]) ).
fof(f1132,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(or(X0,X0),X1))) ),
inference(resolution,[],[f945,f784]) ).
fof(f18297,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(not(X0))))
| ~ spl2_7 ),
inference(resolution,[],[f18248,f1867]) ).
fof(f92662,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[],[f92525,f277]) ).
fof(f98732,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97893]) ).
fof(f97893,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18125]) ).
fof(f18125,plain,
( ! [X0] : is_a_theorem(not(not(equiv(X0,X0))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f9835]) ).
fof(f98731,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97895]) ).
fof(f97895,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f27591]) ).
fof(f27591,plain,
( ! [X0] : is_a_theorem(not(not(not(not(equiv(X0,X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f18629,f18147]) ).
fof(f98730,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97896]) ).
fof(f97896,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28258]) ).
fof(f28258,plain,
( ! [X0] : is_a_theorem(not(not(not(not(strict_equiv(X0,X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f18654,f18147]) ).
fof(f98729,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97901]) ).
fof(f97901,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f95300]) ).
fof(f95300,plain,
( ! [X0] : is_a_theorem(not(not(or(X0,not(X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f93823,f18364]) ).
fof(f93823,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X1)))),
inference(superposition,[],[f92527,f277]) ).
fof(f98728,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97906]) ).
fof(f97906,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f41539]) ).
fof(f98727,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97907]) ).
fof(f97907,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f41567]) ).
fof(f98726,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97908]) ).
fof(f97908,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18129]) ).
fof(f18129,plain,
( ! [X0] : is_a_theorem(not(not(strict_equiv(X0,X0))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f9852]) ).
fof(f98725,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97911]) ).
fof(f97911,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18132]) ).
fof(f18132,plain,
( ! [X0] : is_a_theorem(not(not(possibly(equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f11762]) ).
fof(f98724,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97912]) ).
fof(f97912,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18133]) ).
fof(f18133,plain,
( ! [X0] : is_a_theorem(not(not(possibly(strict_equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f12144]) ).
fof(f98723,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97917]) ).
fof(f97917,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2727]) ).
fof(f2727,plain,
! [X0] : is_a_theorem(not(and(not(X0),or(X0,X0)))),
inference(superposition,[],[f728,f279]) ).
fof(f98722,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97918]) ).
fof(f97918,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2731]) ).
fof(f2731,plain,
! [X0,X1] : is_a_theorem(not(and(and(not(X0),not(X1)),or(X0,X1)))),
inference(superposition,[],[f727,f279]) ).
fof(f98721,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97919]) ).
fof(f97919,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2778]) ).
fof(f2778,plain,
! [X2,X0,X1] : is_a_theorem(not(and(and(and(not(X0),not(X1)),X2),or(X0,X1)))),
inference(superposition,[],[f232,f279]) ).
fof(f98720,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97920]) ).
fof(f97920,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2779]) ).
fof(f2779,plain,
! [X2,X0,X1] : is_a_theorem(not(and(and(X0,and(not(X1),not(X2))),or(X1,X2)))),
inference(superposition,[],[f233,f279]) ).
fof(f98719,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97921]) ).
fof(f97921,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2786]) ).
fof(f2786,plain,
! [X0,X1] : is_a_theorem(not(and(necessarily(and(not(X0),not(X1))),or(X0,X1)))),
inference(superposition,[],[f225,f279]) ).
fof(f98718,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97928]) ).
fof(f97928,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23113]) ).
fof(f23113,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(equiv(X0,X0)),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f19263,f10261]) ).
fof(f98717,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97929]) ).
fof(f97929,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23121]) ).
fof(f23121,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(strict_equiv(X0,X0)),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f19263,f10284]) ).
fof(f98716,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97931]) ).
fof(f97931,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23180]) ).
fof(f23180,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(possibly(equiv(X0,X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f19264,f11762]) ).
fof(f98715,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97932]) ).
fof(f97932,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23181]) ).
fof(f23181,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(possibly(strict_equiv(X0,X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f19264,f12144]) ).
fof(f98714,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97935]) ).
fof(f97935,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28218]) ).
fof(f28218,plain,
( ! [X0,X1] : is_a_theorem(not(and(necessarily(not(equiv(X0,X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f18632,f19268]) ).
fof(f98713,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97936]) ).
fof(f97936,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28468]) ).
fof(f28468,plain,
( ! [X0,X1] : is_a_theorem(not(and(necessarily(not(strict_equiv(X0,X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f18657,f19268]) ).
fof(f98712,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97939]) ).
fof(f97939,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28217]) ).
fof(f28217,plain,
( ! [X0,X1] : is_a_theorem(not(and(X0,necessarily(not(equiv(X1,X1))))))
| ~ spl2_7 ),
inference(resolution,[],[f18632,f19173]) ).
fof(f98711,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97940]) ).
fof(f97940,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28467]) ).
fof(f28467,plain,
( ! [X0,X1] : is_a_theorem(not(and(X0,necessarily(not(strict_equiv(X1,X1))))))
| ~ spl2_7 ),
inference(resolution,[],[f18657,f19173]) ).
fof(f98710,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97946]) ).
fof(f97946,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28222]) ).
fof(f28222,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(not(equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f18632,f18407]) ).
fof(f98709,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97947]) ).
fof(f97947,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28472]) ).
fof(f28472,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f18657,f18407]) ).
fof(f98708,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97949]) ).
fof(f97949,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28223]) ).
fof(f28223,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(X0,not(equiv(X1,X1))))))
| ~ spl2_7 ),
inference(resolution,[],[f18632,f18406]) ).
fof(f98707,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97950]) ).
fof(f97950,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28473]) ).
fof(f28473,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(X0,not(strict_equiv(X1,X1))))))
| ~ spl2_7 ),
inference(resolution,[],[f18657,f18406]) ).
fof(f98706,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97955]) ).
fof(f97955,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23602]) ).
fof(f23602,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(equiv(X0,X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f20196,f10261]) ).
fof(f98705,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97956]) ).
fof(f97956,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23610]) ).
fof(f23610,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(strict_equiv(X0,X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f20196,f10284]) ).
fof(f98704,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97958]) ).
fof(f97958,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23667]) ).
fof(f23667,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(possibly(equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f20197,f11762]) ).
fof(f98703,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97959]) ).
fof(f97959,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23668]) ).
fof(f23668,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(possibly(strict_equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f20197,f12144]) ).
fof(f98702,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97962]) ).
fof(f97962,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28221]) ).
fof(f28221,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f18632,f20201]) ).
fof(f98701,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97963]) ).
fof(f97963,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28471]) ).
fof(f28471,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f18657,f20201]) ).
fof(f98700,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97971]) ).
fof(f97971,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f21936]) ).
fof(f21936,plain,
( ! [X0] : is_a_theorem(not(possibly(not(equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18164,f18123]) ).
fof(f98699,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97972]) ).
fof(f97972,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f21937]) ).
fof(f21937,plain,
( ! [X0] : is_a_theorem(not(possibly(not(strict_equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18164,f18127]) ).
fof(f98698,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97974]) ).
fof(f97974,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f32261]) ).
fof(f98697,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97975]) ).
fof(f97975,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f32366]) ).
fof(f98696,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97977]) ).
fof(f97977,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f36036]) ).
fof(f36036,plain,
( ! [X0] : is_a_theorem(not(possibly(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f23601,f18164]) ).
fof(f23601,plain,
( ! [X0] : is_a_theorem(necessarily(not(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f20196,f10260]) ).
fof(f98695,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f97978]) ).
fof(f97978,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f36057]) ).
fof(f36057,plain,
( ! [X0] : is_a_theorem(not(possibly(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f23609,f18164]) ).
fof(f23609,plain,
( ! [X0] : is_a_theorem(necessarily(not(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f20196,f10283]) ).
fof(f98694,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97998]) ).
fof(f97998,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9839]) ).
fof(f9839,plain,
! [X0] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f9821,f2683]) ).
fof(f2683,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(and(X0,X0)) ),
inference(resolution,[],[f2180,f2147]) ).
fof(f2147,plain,
! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(resolution,[],[f1853,f234]) ).
fof(f1853,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1165,f247]) ).
fof(f1165,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1164,f218]) ).
fof(f1164,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(forward_demodulation,[],[f1128,f218]) ).
fof(f1128,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,implies(X0,X1))))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f945,f238]) ).
fof(f98693,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f97999]) ).
fof(f97999,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11215]) ).
fof(f11215,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),equiv(X1,X1))),
inference(resolution,[],[f10400,f9835]) ).
fof(f98692,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98000]) ).
fof(f98000,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11216]) ).
fof(f11216,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),strict_equiv(X1,X1))),
inference(resolution,[],[f10400,f9852]) ).
fof(f98691,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98002]) ).
fof(f98002,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12769]) ).
fof(f12769,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),possibly(equiv(X1,X1)))),
inference(resolution,[],[f11975,f9835]) ).
fof(f98690,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98003]) ).
fof(f98003,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12773]) ).
fof(f12773,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f11975,f9852]) ).
fof(f98689,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98012]) ).
fof(f98012,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11262]) ).
fof(f11262,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),equiv(X1,X1))),
inference(resolution,[],[f10704,f9835]) ).
fof(f98688,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98013]) ).
fof(f98013,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9856]) ).
fof(f9856,plain,
! [X0] : is_a_theorem(and(strict_equiv(X0,X0),strict_equiv(X0,X0))),
inference(resolution,[],[f9833,f2683]) ).
fof(f98687,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98014]) ).
fof(f98014,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11263]) ).
fof(f11263,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),strict_equiv(X1,X1))),
inference(resolution,[],[f10704,f9852]) ).
fof(f98686,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98016]) ).
fof(f98016,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12876]) ).
fof(f12876,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),possibly(equiv(X1,X1)))),
inference(resolution,[],[f12284,f9835]) ).
fof(f98685,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98017]) ).
fof(f98017,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12880]) ).
fof(f12880,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12284,f9852]) ).
fof(f98684,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98024]) ).
fof(f98024,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f15031]) ).
fof(f15031,plain,
! [X0,X1] : is_a_theorem(and(possibly(equiv(X0,X0)),equiv(X1,X1))),
inference(resolution,[],[f14443,f9835]) ).
fof(f98683,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98025]) ).
fof(f98025,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f15035]) ).
fof(f15035,plain,
! [X0,X1] : is_a_theorem(and(possibly(equiv(X0,X0)),strict_equiv(X1,X1))),
inference(resolution,[],[f14443,f9852]) ).
fof(f98682,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98027]) ).
fof(f98027,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f15075]) ).
fof(f15075,plain,
! [X0,X1] : is_a_theorem(and(possibly(strict_equiv(X0,X0)),equiv(X1,X1))),
inference(resolution,[],[f14896,f9835]) ).
fof(f98681,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98028]) ).
fof(f98028,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f15079]) ).
fof(f15079,plain,
! [X0,X1] : is_a_theorem(and(possibly(strict_equiv(X0,X0)),strict_equiv(X1,X1))),
inference(resolution,[],[f14896,f9852]) ).
fof(f98680,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98033]) ).
fof(f98033,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92662]) ).
fof(f98679,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98039]) ).
fof(f98039,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f294]) ).
fof(f98678,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98040]) ).
fof(f98040,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f295]) ).
fof(f295,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,and(not(X0),X1)))),
inference(superposition,[],[f234,f277]) ).
fof(f98677,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98042]) ).
fof(f98042,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20963]) ).
fof(f20963,plain,
( ! [X0,X1] : is_a_theorem(or(X0,implies(necessarily(not(not(X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f19295,f881]) ).
fof(f98676,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98043]) ).
fof(f98043,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9821]) ).
fof(f98675,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98044]) ).
fof(f98044,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f742]) ).
fof(f98674,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98047]) ).
fof(f98047,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f27601]) ).
fof(f27601,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(not(equiv(X1,X1)))))
| ~ spl2_7 ),
inference(resolution,[],[f18629,f298]) ).
fof(f298,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[],[f229,f277]) ).
fof(f98673,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98048]) ).
fof(f98048,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18147]) ).
fof(f98672,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98049]) ).
fof(f98049,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28269]) ).
fof(f28269,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl2_7 ),
inference(resolution,[],[f18654,f298]) ).
fof(f98671,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98050]) ).
fof(f98050,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2795]) ).
fof(f98670,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98051]) ).
fof(f98051,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19265]) ).
fof(f19265,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(and(not(not(X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f18301,f881]) ).
fof(f98669,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98052]) ).
fof(f98052,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20198]) ).
fof(f20198,plain,
( ! [X0] : is_a_theorem(or(X0,not(necessarily(necessarily(not(not(X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f18408,f881]) ).
fof(f98668,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98058]) ).
fof(f98058,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10412]) ).
fof(f10412,plain,
! [X0,X1] : is_a_theorem(or(X0,and(equiv(X1,X1),not(X0)))),
inference(resolution,[],[f9835,f297]) ).
fof(f98667,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98059]) ).
fof(f98059,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f755]) ).
fof(f755,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f728,f277]) ).
fof(f98666,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98060]) ).
fof(f98060,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10716]) ).
fof(f10716,plain,
! [X0,X1] : is_a_theorem(or(X0,and(strict_equiv(X1,X1),not(X0)))),
inference(resolution,[],[f9852,f297]) ).
fof(f98665,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98062]) ).
fof(f98062,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f298]) ).
fof(f98664,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98063]) ).
fof(f98063,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f93823]) ).
fof(f98663,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98064]) ).
fof(f98064,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f437]) ).
fof(f437,plain,
! [X0,X1] : is_a_theorem(or(X1,or(X0,and(not(X1),not(X0))))),
inference(superposition,[],[f295,f277]) ).
fof(f98662,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98069]) ).
fof(f98069,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f299]) ).
fof(f299,plain,
! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1))),
inference(superposition,[],[f230,f277]) ).
fof(f98661,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98070]) ).
fof(f98070,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f300]) ).
fof(f300,plain,
! [X0] : is_a_theorem(or(X0,necessarily(possibly(not(X0))))),
inference(superposition,[],[f226,f277]) ).
fof(f98660,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98077]) ).
fof(f98077,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45627]) ).
fof(f45627,plain,
( ! [X2,X0,X1] : is_a_theorem(or(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f41539,f20650]) ).
fof(f20650,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X1,X0)) )
| ~ spl2_7 ),
inference(resolution,[],[f19184,f2963]) ).
fof(f2963,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(X0) ),
inference(resolution,[],[f2946,f270]) ).
fof(f270,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f253,f242]) ).
fof(f253,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,and(X1,X0)))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f242,f234]) ).
fof(f19184,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X1)))
| ~ spl2_7 ),
inference(superposition,[],[f18300,f222]) ).
fof(f98659,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98078]) ).
fof(f98078,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45657]) ).
fof(f45657,plain,
( ! [X2,X0,X1] : is_a_theorem(or(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f41567,f20650]) ).
fof(f98658,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98081]) ).
fof(f98081,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f9833]) ).
fof(f98657,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98085]) ).
fof(f98085,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11730]) ).
fof(f98656,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98086]) ).
fof(f98086,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f6093]) ).
fof(f6093,plain,
! [X0] : is_a_theorem(or(X0,possibly(not(X0)))),
inference(superposition,[],[f6057,f277]) ).
fof(f98655,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98087]) ).
fof(f98087,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12112]) ).
fof(f98654,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98088]) ).
fof(f98088,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92679]) ).
fof(f92679,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X0),X1)),
inference(resolution,[],[f92662,f17194]) ).
fof(f17194,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f8201,f737]) ).
fof(f737,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f736,f277]) ).
fof(f736,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f734,f277]) ).
fof(f734,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f358,f277]) ).
fof(f8201,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f8197,f277]) ).
fof(f8197,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5931,f277]) ).
fof(f5931,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1715,f230]) ).
fof(f98653,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98089]) ).
fof(f98089,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19278]) ).
fof(f98652,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98094]) ).
fof(f98094,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19183]) ).
fof(f19183,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),not(X1)))
| ~ spl2_7 ),
inference(superposition,[],[f18300,f219]) ).
fof(f98651,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98095]) ).
fof(f98095,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18149]) ).
fof(f18149,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1))))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f18121,f277]) ).
fof(f18121,plain,
( ! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),and(X0,not(X1))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f1332]) ).
fof(f98650,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98096]) ).
fof(f98096,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19295]) ).
fof(f98649,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98097]) ).
fof(f98097,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20966]) ).
fof(f98648,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98098]) ).
fof(f98098,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24919]) ).
fof(f24919,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(necessarily(necessarily(X0))),X1),X0))
| ~ spl2_7 ),
inference(resolution,[],[f20966,f6084]) ).
fof(f98647,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98099]) ).
fof(f98099,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19293]) ).
fof(f98646,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98100]) ).
fof(f98100,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19294]) ).
fof(f98645,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98101]) ).
fof(f98101,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23554]) ).
fof(f23554,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,necessarily(X1)),X2),X1))
| ~ spl2_7 ),
inference(resolution,[],[f19293,f6084]) ).
fof(f98644,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98102]) ).
fof(f98102,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23574]) ).
fof(f23574,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(necessarily(X0),X1),X2),X0))
| ~ spl2_7 ),
inference(resolution,[],[f19294,f6084]) ).
fof(f98643,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98103]) ).
fof(f98103,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20964]) ).
fof(f20964,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(necessarily(and(X0,X1)),X2),X1))
| ~ spl2_7 ),
inference(resolution,[],[f19295,f8844]) ).
fof(f98642,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98104]) ).
fof(f98104,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20965]) ).
fof(f20965,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(necessarily(and(X0,X1)),X2),X0))
| ~ spl2_7 ),
inference(resolution,[],[f19295,f8263]) ).
fof(f98641,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98106]) ).
fof(f98106,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19186]) ).
fof(f19186,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,necessarily(not(X1))),possibly(X1)))
| ~ spl2_7 ),
inference(superposition,[],[f18300,f263]) ).
fof(f98640,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98107]) ).
fof(f98107,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10417]) ).
fof(f10417,plain,
! [X0,X1] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(resolution,[],[f9835,f230]) ).
fof(f98639,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98110]) ).
fof(f98110,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18248]) ).
fof(f98638,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98111]) ).
fof(f98111,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19176]) ).
fof(f19176,plain,
( ! [X0,X1] : is_a_theorem(or(not(equiv(X0,X1)),implies(X1,X0)))
| ~ spl2_7 ),
inference(superposition,[],[f18300,f223]) ).
fof(f98637,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98112]) ).
fof(f98112,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19271]) ).
fof(f19271,plain,
( ! [X0,X1] : is_a_theorem(or(not(equiv(X0,X1)),implies(X0,X1)))
| ~ spl2_7 ),
inference(superposition,[],[f18301,f223]) ).
fof(f98636,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98114]) ).
fof(f98114,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f27607]) ).
fof(f27607,plain,
( ! [X0,X1] : is_a_theorem(or(not(not(equiv(X0,X0))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18629,f299]) ).
fof(f98635,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98115]) ).
fof(f98115,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28275]) ).
fof(f28275,plain,
( ! [X0,X1] : is_a_theorem(or(not(not(strict_equiv(X0,X0))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18654,f299]) ).
fof(f98634,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98116]) ).
fof(f98116,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18300]) ).
fof(f98633,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98117]) ).
fof(f98117,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18301]) ).
fof(f98632,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98118]) ).
fof(f98118,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19173]) ).
fof(f98631,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98119]) ).
fof(f98119,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22741]) ).
fof(f22741,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,necessarily(necessarily(X1)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f19173,f6084]) ).
fof(f98630,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98120]) ).
fof(f98120,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19171]) ).
fof(f19171,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(X0,and(X1,X2))),X2))
| ~ spl2_7 ),
inference(resolution,[],[f18300,f8844]) ).
fof(f98629,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98121]) ).
fof(f98121,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19172]) ).
fof(f19172,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(X0,and(X1,X2))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18300,f8263]) ).
fof(f98628,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98122]) ).
fof(f98122,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19268]) ).
fof(f98627,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98123]) ).
fof(f98123,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23229]) ).
fof(f23229,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(necessarily(necessarily(X0)),X1)),X0))
| ~ spl2_7 ),
inference(resolution,[],[f19268,f6084]) ).
fof(f98626,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98124]) ).
fof(f98124,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19266]) ).
fof(f19266,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(and(X0,X1),X2)),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18301,f8844]) ).
fof(f98625,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98125]) ).
fof(f98125,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19267]) ).
fof(f19267,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(and(X0,X1),X2)),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18301,f8263]) ).
fof(f98624,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98126]) ).
fof(f98126,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18302]) ).
fof(f98623,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98127]) ).
fof(f98127,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18408]) ).
fof(f98622,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98128]) ).
fof(f98128,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20201]) ).
fof(f98621,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98129]) ).
fof(f98129,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23714]) ).
fof(f23714,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(necessarily(necessarily(X0))))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f20201,f6084]) ).
fof(f98620,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98130]) ).
fof(f98130,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20200]) ).
fof(f20200,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(necessarily(and(X0,X1)))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18408,f8263]) ).
fof(f98619,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98131]) ).
fof(f98131,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18407]) ).
fof(f98618,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98132]) ).
fof(f98132,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22672]) ).
fof(f22672,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(necessarily(X0),X1))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f18407,f6084]) ).
fof(f98617,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98133]) ).
fof(f98133,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18406]) ).
fof(f98616,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98134]) ).
fof(f98134,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22653]) ).
fof(f22653,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,necessarily(X1)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18406,f6084]) ).
fof(f98615,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98135]) ).
fof(f98135,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20199]) ).
fof(f20199,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(necessarily(and(X0,X1)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f18408,f8844]) ).
fof(f98614,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98136]) ).
fof(f98136,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18410]) ).
fof(f18410,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_implies(X0,X1)),implies(X0,X1)))
| ~ spl2_7 ),
inference(superposition,[],[f18302,f218]) ).
fof(f98613,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98137]) ).
fof(f98137,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19175]) ).
fof(f19175,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_equiv(X0,X1)),strict_implies(X1,X0)))
| ~ spl2_7 ),
inference(superposition,[],[f18300,f220]) ).
fof(f98612,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98138]) ).
fof(f98138,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19270]) ).
fof(f19270,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_equiv(X0,X1)),strict_implies(X0,X1)))
| ~ spl2_7 ),
inference(superposition,[],[f18301,f220]) ).
fof(f98611,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98142]) ).
fof(f98142,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f746]) ).
fof(f746,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X0,X1))),
inference(superposition,[],[f742,f219]) ).
fof(f98610,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98143]) ).
fof(f98143,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2799]) ).
fof(f2799,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,or(X1,X2)),implies(implies(and(not(X1),not(X2)),X3),implies(X0,X3)))),
inference(forward_demodulation,[],[f2742,f277]) ).
fof(f2742,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(not(and(X0,or(X1,X2))),implies(implies(and(not(X1),not(X2)),X3),implies(X0,X3)))),
inference(superposition,[],[f243,f279]) ).
fof(f98609,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98144]) ).
fof(f98144,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2797]) ).
fof(f2797,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,or(X1,X2)),implies(implies(and(not(X1),not(X2)),X0),equiv(X0,and(not(X1),not(X2)))))),
inference(forward_demodulation,[],[f2739,f277]) ).
fof(f2739,plain,
! [X2,X0,X1] : is_a_theorem(implies(not(and(X0,or(X1,X2))),implies(implies(and(not(X1),not(X2)),X0),equiv(X0,and(not(X1),not(X2)))))),
inference(superposition,[],[f240,f279]) ).
fof(f98608,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98149]) ).
fof(f98149,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2807]) ).
fof(f2807,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X3,or(X1,X2)),or(and(X0,or(X1,X2)),not(and(or(X3,X0),or(X1,X2)))))),
inference(forward_demodulation,[],[f2806,f277]) ).
fof(f2806,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(not(and(X3,or(X1,X2))),or(and(X0,or(X1,X2)),not(and(or(X3,X0),or(X1,X2)))))),
inference(forward_demodulation,[],[f2805,f279]) ).
fof(f2805,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(X3,and(not(X1),not(X2))),or(and(X0,or(X1,X2)),not(and(or(X3,X0),or(X1,X2)))))),
inference(forward_demodulation,[],[f2804,f279]) ).
fof(f2804,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(X3,and(not(X1),not(X2))),or(and(X0,or(X1,X2)),implies(or(X3,X0),and(not(X1),not(X2)))))),
inference(forward_demodulation,[],[f2745,f277]) ).
fof(f2745,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(X3,and(not(X1),not(X2))),implies(not(and(X0,or(X1,X2))),implies(or(X3,X0),and(not(X1),not(X2)))))),
inference(superposition,[],[f244,f279]) ).
fof(f98607,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98152]) ).
fof(f98152,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19184]) ).
fof(f98606,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98153]) ).
fof(f98153,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19279]) ).
fof(f19279,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0)))
| ~ spl2_7 ),
inference(superposition,[],[f18301,f222]) ).
fof(f98605,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98154]) ).
fof(f98154,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19187]) ).
fof(f19187,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,necessarily(not(X1))),possibly(X1)))
| ~ spl2_7 ),
inference(superposition,[],[f18300,f274]) ).
fof(f98604,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98155]) ).
fof(f98155,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f95299]) ).
fof(f95299,plain,
! [X0,X1] : is_a_theorem(or(or(X0,not(X0)),X1)),
inference(resolution,[],[f93823,f17194]) ).
fof(f98603,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98156]) ).
fof(f98156,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f301]) ).
fof(f301,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),implies(X1,possibly(X0)))),
inference(superposition,[],[f294,f221]) ).
fof(f98602,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98157]) ).
fof(f98157,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f305]) ).
fof(f305,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),or(X1,possibly(X0)))),
inference(superposition,[],[f298,f221]) ).
fof(f98601,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98158]) ).
fof(f98158,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f308]) ).
fof(f308,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),or(possibly(X0),X1))),
inference(superposition,[],[f299,f221]) ).
fof(f98600,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98159]) ).
fof(f98159,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f311]) ).
fof(f311,plain,
! [X0] : is_a_theorem(or(necessarily(not(X0)),necessarily(possibly(possibly(X0))))),
inference(superposition,[],[f300,f221]) ).
fof(f98599,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98164]) ).
fof(f98164,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45621]) ).
fof(f45621,plain,
( ! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(equiv(X0,X0)),X1),X2))
| ~ spl2_7 ),
inference(resolution,[],[f41539,f350]) ).
fof(f350,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f344,f277]) ).
fof(f344,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f329,f250]) ).
fof(f250,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f242,f229]) ).
fof(f98598,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98165]) ).
fof(f98165,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45651]) ).
fof(f45651,plain,
( ! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl2_7 ),
inference(resolution,[],[f41567,f350]) ).
fof(f98597,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98168]) ).
fof(f98168,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10721]) ).
fof(f10721,plain,
! [X0,X1] : is_a_theorem(or(strict_equiv(X0,X0),X1)),
inference(resolution,[],[f9852,f230]) ).
fof(f98596,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98171]) ).
fof(f98171,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f14465]) ).
fof(f14465,plain,
! [X0,X1] : is_a_theorem(or(possibly(equiv(X0,X0)),X1)),
inference(resolution,[],[f11762,f230]) ).
fof(f98595,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98172]) ).
fof(f98172,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f14918]) ).
fof(f14918,plain,
! [X0,X1] : is_a_theorem(or(possibly(strict_equiv(X0,X0)),X1)),
inference(resolution,[],[f12144,f230]) ).
fof(f98594,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98173]) ).
fof(f98173,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18413]) ).
fof(f18413,plain,
( ! [X0] : is_a_theorem(or(possibly(X0),not(X0)))
| ~ spl2_7 ),
inference(superposition,[],[f18302,f221]) ).
fof(f98593,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98174]) ).
fof(f98174,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18150]) ).
fof(f18150,plain,
( ! [X0] : is_a_theorem(or(possibly(X0),necessarily(not(X0))))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f18130,f277]) ).
fof(f18130,plain,
( ! [X0] : is_a_theorem(implies(not(possibly(X0)),necessarily(not(X0))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f665]) ).
fof(f665,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(X1)))
| is_a_theorem(implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f329,f281]) ).
fof(f98592,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98176]) ).
fof(f98176,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f5877]) ).
fof(f5877,plain,
! [X0] : is_a_theorem(necessarily(equiv(X0,X0))),
inference(subsumption_resolution,[],[f5870,f727]) ).
fof(f5870,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(resolution,[],[f5813,f2151]) ).
fof(f2151,plain,
! [X0] : is_a_theorem(strict_implies(implies(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f1853,f240]) ).
fof(f98591,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98181]) ).
fof(f98181,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18123]) ).
fof(f98590,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98182]) ).
fof(f98182,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18127]) ).
fof(f98589,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98184]) ).
fof(f98184,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23112]) ).
fof(f98588,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98185]) ).
fof(f98185,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23120]) ).
fof(f98587,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98188]) ).
fof(f98188,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23601]) ).
fof(f98586,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98189]) ).
fof(f98189,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23609]) ).
fof(f98585,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98201]) ).
fof(f98201,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11685]) ).
fof(f11685,plain,
! [X0] : is_a_theorem(necessarily(and(equiv(X0,X0),equiv(X0,X0)))),
inference(resolution,[],[f10250,f728]) ).
fof(f98584,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98202]) ).
fof(f98202,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11688]) ).
fof(f11688,plain,
! [X0,X1] : is_a_theorem(necessarily(and(equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10250,f10400]) ).
fof(f98583,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98204]) ).
fof(f98204,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12073]) ).
fof(f12073,plain,
! [X0,X1] : is_a_theorem(necessarily(and(equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10273,f10400]) ).
fof(f98582,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98205]) ).
fof(f98205,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12070]) ).
fof(f12070,plain,
! [X0] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),strict_equiv(X0,X0)))),
inference(resolution,[],[f10273,f728]) ).
fof(f98581,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98206]) ).
fof(f98206,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12074]) ).
fof(f12074,plain,
! [X0,X1] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10273,f10704]) ).
fof(f98580,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98208]) ).
fof(f98208,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11689]) ).
fof(f11689,plain,
! [X0,X1] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10250,f10704]) ).
fof(f98579,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98215]) ).
fof(f98215,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11701]) ).
fof(f98578,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98216]) ).
fof(f98216,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12086]) ).
fof(f98577,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98219]) ).
fof(f98219,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f5891]) ).
fof(f5891,plain,
! [X0] : is_a_theorem(necessarily(strict_implies(X0,X0))),
inference(resolution,[],[f5878,f1156]) ).
fof(f1156,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X1,X0))) ),
inference(resolution,[],[f945,f425]) ).
fof(f5878,plain,
! [X0] : is_a_theorem(necessarily(strict_equiv(X0,X0))),
inference(subsumption_resolution,[],[f5875,f1913]) ).
fof(f5875,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(necessarily(strict_equiv(X0,X0))) ),
inference(resolution,[],[f5813,f2156]) ).
fof(f2156,plain,
! [X0] : is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(resolution,[],[f1853,f426]) ).
fof(f98576,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98221]) ).
fof(f98221,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45625]) ).
fof(f45625,plain,
( ! [X0,X1] : is_a_theorem(necessarily(strict_implies(not(equiv(X0,X0)),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f41539,f18329]) ).
fof(f18329,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(necessarily(X0)) )
| ~ spl2_7 ),
inference(resolution,[],[f18250,f5813]) ).
fof(f98575,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98222]) ).
fof(f98222,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45655]) ).
fof(f45655,plain,
( ! [X0,X1] : is_a_theorem(necessarily(strict_implies(not(strict_equiv(X0,X0)),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f41567,f18329]) ).
fof(f98574,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98223]) ).
fof(f98223,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f5878]) ).
fof(f98573,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98233]) ).
fof(f98233,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10418]) ).
fof(f10418,plain,
! [X0] : is_a_theorem(necessarily(possibly(equiv(X0,X0)))),
inference(resolution,[],[f9835,f226]) ).
fof(f98572,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98236]) ).
fof(f98236,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f27608]) ).
fof(f27608,plain,
( ! [X0] : is_a_theorem(necessarily(possibly(not(not(equiv(X0,X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f18629,f300]) ).
fof(f98571,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98237]) ).
fof(f98237,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28276]) ).
fof(f28276,plain,
( ! [X0] : is_a_theorem(necessarily(possibly(not(not(strict_equiv(X0,X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f18654,f300]) ).
fof(f98570,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98246]) ).
fof(f98246,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10722]) ).
fof(f10722,plain,
! [X0] : is_a_theorem(necessarily(possibly(strict_equiv(X0,X0)))),
inference(resolution,[],[f9852,f226]) ).
fof(f98569,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98249]) ).
fof(f98249,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f14466]) ).
fof(f14466,plain,
! [X0] : is_a_theorem(necessarily(possibly(possibly(equiv(X0,X0))))),
inference(resolution,[],[f11762,f226]) ).
fof(f98568,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98250]) ).
fof(f98250,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f14919]) ).
fof(f14919,plain,
! [X0] : is_a_theorem(necessarily(possibly(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f12144,f226]) ).
fof(f98567,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98251]) ).
fof(f98251,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f1913]) ).
fof(f98566,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98252]) ).
fof(f98252,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18250]) ).
fof(f98565,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98253]) ).
fof(f98253,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23115]) ).
fof(f23115,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),X0))
| ~ spl2_7 ),
inference(resolution,[],[f19263,f1181]) ).
fof(f98564,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98254]) ).
fof(f98254,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f32582]) ).
fof(f32582,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(necessarily(not(not(X0))),X1),X0))
| ~ spl2_7 ),
inference(resolution,[],[f23223,f1181]) ).
fof(f98563,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98255]) ).
fof(f98255,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23604]) ).
fof(f23604,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(necessarily(not(not(X0)))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f20196,f1181]) ).
fof(f98562,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98256]) ).
fof(f98256,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f38275]) ).
fof(f38275,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(necessarily(necessarily(not(not(X0))))),X0))
| ~ spl2_7 ),
inference(resolution,[],[f23708,f1181]) ).
fof(f98561,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98257]) ).
fof(f98257,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f31726]) ).
fof(f31726,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(and(not(not(X0)),X1)),X0))
| ~ spl2_7 ),
inference(resolution,[],[f22666,f1181]) ).
fof(f98560,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98267]) ).
fof(f98267,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11726]) ).
fof(f11726,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(equiv(X0,X0)),X1)),
inference(forward_demodulation,[],[f11700,f287]) ).
fof(f11700,plain,
! [X0,X1] : is_a_theorem(necessarily(or(equiv(X0,X0),X1))),
inference(resolution,[],[f10250,f230]) ).
fof(f98559,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98268]) ).
fof(f98268,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12108]) ).
fof(f12108,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(strict_equiv(X0,X0)),X1)),
inference(forward_demodulation,[],[f12085,f287]) ).
fof(f12085,plain,
! [X0,X1] : is_a_theorem(necessarily(or(strict_equiv(X0,X0),X1))),
inference(resolution,[],[f10273,f230]) ).
fof(f98558,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98269]) ).
fof(f98269,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2909]) ).
fof(f2909,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(not(X0),or(X1,X0)),X1)),
inference(resolution,[],[f2795,f1867]) ).
fof(f98557,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98270]) ).
fof(f98270,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f31862]) ).
fof(f31862,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,necessarily(not(not(X1)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f22735,f1181]) ).
fof(f98556,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98280]) ).
fof(f98280,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24830]) ).
fof(f24830,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(equiv(X0,X0))),X1))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f24798,f218]) ).
fof(f24798,plain,
( ! [X0,X1] : is_a_theorem(necessarily(implies(necessarily(not(equiv(X0,X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f20961,f10260]) ).
fof(f98555,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98281]) ).
fof(f98281,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24831]) ).
fof(f24831,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(strict_equiv(X0,X0))),X1))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f24804,f218]) ).
fof(f24804,plain,
( ! [X0,X1] : is_a_theorem(necessarily(implies(necessarily(not(strict_equiv(X0,X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f20961,f10283]) ).
fof(f98554,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98283]) ).
fof(f98283,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f42083]) ).
fof(f42083,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(possibly(equiv(X0,X0)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f24807,f1853]) ).
fof(f98553,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98284]) ).
fof(f98284,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f42108]) ).
fof(f42108,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(possibly(strict_equiv(X0,X0)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f24808,f1853]) ).
fof(f98552,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98285]) ).
fof(f98285,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f31547]) ).
fof(f31547,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(and(X0,not(not(X1)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f22647,f1181]) ).
fof(f98551,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98287]) ).
fof(f98287,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f36032]) ).
fof(f36032,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(necessarily(not(equiv(X0,X0)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f23601,f1870]) ).
fof(f98550,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98288]) ).
fof(f98288,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f36053]) ).
fof(f36053,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(necessarily(not(strict_equiv(X0,X0)))),X1))
| ~ spl2_7 ),
inference(resolution,[],[f23609,f1870]) ).
fof(f98549,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98293]) ).
fof(f98293,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f32257]) ).
fof(f32257,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(equiv(X0,X0)),X1),X2))
| ~ spl2_7 ),
inference(resolution,[],[f23112,f1870]) ).
fof(f98548,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98294]) ).
fof(f98294,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f32362]) ).
fof(f32362,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl2_7 ),
inference(resolution,[],[f23120,f1870]) ).
fof(f98547,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98298]) ).
fof(f98298,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f35086]) ).
fof(f35086,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X0,not(equiv(X1,X1))),X2))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f35052,f218]) ).
fof(f35052,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(implies(and(X0,not(equiv(X1,X1))),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f23548,f10260]) ).
fof(f23548,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,implies(and(X1,not(X0)),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f19293,f1867]) ).
fof(f98546,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98299]) ).
fof(f98299,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f35087]) ).
fof(f35087,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X0,not(strict_equiv(X1,X1))),X2))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f35058,f218]) ).
fof(f35058,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(implies(and(X0,not(strict_equiv(X1,X1))),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f23548,f10283]) ).
fof(f98545,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98300]) ).
fof(f98300,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2153]) ).
fof(f2153,plain,
! [X0,X1] : is_a_theorem(strict_implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(resolution,[],[f1853,f244]) ).
fof(f98544,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98301]) ).
fof(f98301,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19191]) ).
fof(f19191,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X0)))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f19168,f219]) ).
fof(f19168,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(X1,not(X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18300,f1867]) ).
fof(f98543,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98302]) ).
fof(f98302,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f93627]) ).
fof(f93627,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X1))),
inference(resolution,[],[f92679,f1867]) ).
fof(f98542,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98308]) ).
fof(f98308,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20961]) ).
fof(f98541,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98309]) ).
fof(f98309,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24913]) ).
fof(f24913,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(necessarily(necessarily(not(X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f20966,f1867]) ).
fof(f98540,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98310]) ).
fof(f98310,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23548]) ).
fof(f98539,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98311]) ).
fof(f98311,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23568]) ).
fof(f23568,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,implies(and(not(X0),X1),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f19294,f1867]) ).
fof(f98538,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98312]) ).
fof(f98312,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19327]) ).
fof(f19327,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(X0)),implies(possibly(X0),X1)))
| ~ spl2_7 ),
inference(superposition,[],[f19303,f281]) ).
fof(f19303,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,or(X0,X1)))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f19290,f277]) ).
fof(f19290,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(not(X0),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f19278,f1867]) ).
fof(f98537,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98313]) ).
fof(f98313,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2151]) ).
fof(f98536,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98314]) ).
fof(f98314,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10441]) ).
fof(f10441,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,equiv(X1,X1))),
inference(resolution,[],[f10417,f1867]) ).
fof(f98535,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98316]) ).
fof(f98316,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18297]) ).
fof(f98534,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98318]) ).
fof(f98318,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28083]) ).
fof(f28083,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(not(equiv(X1,X1)))))
| ~ spl2_7 ),
inference(resolution,[],[f27591,f1906]) ).
fof(f1906,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f1886,f1181]) ).
fof(f98533,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98319]) ).
fof(f98319,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f28329]) ).
fof(f28329,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl2_7 ),
inference(resolution,[],[f28258,f1906]) ).
fof(f98532,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98320]) ).
fof(f98320,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19263]) ).
fof(f98531,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98321]) ).
fof(f98321,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22735]) ).
fof(f98530,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98322]) ).
fof(f98322,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23223]) ).
fof(f98529,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98323]) ).
fof(f98323,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f20196]) ).
fof(f98528,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98324]) ).
fof(f98324,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23708]) ).
fof(f98527,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98325]) ).
fof(f98325,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22647]) ).
fof(f98526,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98326]) ).
fof(f98326,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f22666]) ).
fof(f98525,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98327]) ).
fof(f98327,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18382]) ).
fof(f18382,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(not(X0)),not(possibly(X0))))
| ~ spl2_7 ),
inference(superposition,[],[f18297,f221]) ).
fof(f98524,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98328]) ).
fof(f98328,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18444]) ).
fof(f18444,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(not(X0)),not(necessarily(possibly(X0)))))
| ~ spl2_7 ),
inference(superposition,[],[f18418,f245]) ).
fof(f18418,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ spl2_7 ),
inference(forward_demodulation,[],[f18403,f221]) ).
fof(f18403,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(not(X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18302,f1867]) ).
fof(f98523,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98329]) ).
fof(f98329,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2147]) ).
fof(f98522,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98332]) ).
fof(f98332,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11717]) ).
fof(f11717,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,and(equiv(X1,X1),X0))),
inference(forward_demodulation,[],[f11680,f218]) ).
fof(f11680,plain,
! [X0,X1] : is_a_theorem(necessarily(implies(X0,and(equiv(X1,X1),X0)))),
inference(resolution,[],[f10250,f234]) ).
fof(f98521,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98333]) ).
fof(f98333,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12099]) ).
fof(f12099,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,and(strict_equiv(X1,X1),X0))),
inference(forward_demodulation,[],[f12065,f218]) ).
fof(f12065,plain,
! [X0,X1] : is_a_theorem(necessarily(implies(X0,and(strict_equiv(X1,X1),X0)))),
inference(resolution,[],[f10273,f234]) ).
fof(f98520,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98340]) ).
fof(f98340,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19218]) ).
fof(f19218,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X1,or(X0,X1)))
| ~ spl2_7 ),
inference(superposition,[],[f19191,f277]) ).
fof(f98519,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98341]) ).
fof(f98341,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f95596]) ).
fof(f95596,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,or(X1,not(X1)))),
inference(resolution,[],[f95299,f1867]) ).
fof(f98518,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98342]) ).
fof(f98342,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f19303]) ).
fof(f98517,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98347]) ).
fof(f98347,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18332]) ).
fof(f98516,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98350]) ).
fof(f98350,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45622]) ).
fof(f45622,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f41539,f1906]) ).
fof(f98515,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98351]) ).
fof(f98351,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45652]) ).
fof(f45652,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl2_7 ),
inference(resolution,[],[f41567,f1906]) ).
fof(f98514,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98354]) ).
fof(f98354,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2156]) ).
fof(f98513,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98355]) ).
fof(f98355,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f10745]) ).
fof(f10745,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,strict_equiv(X1,X1))),
inference(resolution,[],[f10721,f1867]) ).
fof(f98512,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98356]) ).
fof(f98356,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18418]) ).
fof(f98511,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98359]) ).
fof(f98359,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f14495]) ).
fof(f14495,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f14465,f1867]) ).
fof(f98510,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98360]) ).
fof(f98360,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f14948]) ).
fof(f14948,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f14918,f1867]) ).
fof(f98509,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98361]) ).
fof(f98361,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f2686]) ).
fof(f2686,plain,
! [X0] : is_a_theorem(strict_equiv(X0,X0)),
inference(global_subsumption,[],[f188,f189,f190,f191,f192,f193,f194,f195,f196,f197,f198,f199,f200,f201,f202,f203,f204,f205,f206,f207,f208,f209,f210,f237,f211,f212,f239,f213,f214,f215,f216,f217,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f225,f228,f226,f229,f230,f231,f232,f233,f221,f227,f241,f218,f224,f234,f235,f236,f242,f258,f249,f219,f262,f250,f251,f252,f256,f257,f247,f248,f269,f253,f254,f255,f222,f276,f278,f279,f280,f277,f284,f285,f286,f294,f302,f303,f304,f298,f306,f307,f299,f309,f310,f300,f312,f313,f261,f268,f315,f270,f319,f316,f332,f245,f341,f336,f246,f329,f345,f346,f347,f344,f349,f348,f238,f362,f350,f396,f397,f398,f287,f405,f289,f407,f408,f409,f290,f411,f412,f413,f291,f292,f420,f421,f422,f423,f220,f427,f430,f424,f431,f425,f432,f428,f429,f295,f434,f435,f436,f296,f439,f440,f441,f297,f443,f444,f445,f446,f301,f455,f456,f452,f305,f465,f466,f223,f468,f469,f472,f473,f476,f308,f484,f485,f311,f494,f495,f337,f402,f513,f514,f515,f404,f519,f520,f521,f406,f523,f524,f525,f410,f526,f527,f528,f529,f577,f579,f240,f600,f601,f266,f608,f609,f610,f611,f612,f281,f665,f666,f653,f692,f655,f243,f725,f723,f726,f358,f732,f739,f727,f742,f747,f728,f754,f752,f765,f731,f783,f244,f786,f787,f788,f789,f753,f791,f755,f794,f795,f762,f746,f812,f813,f814,f815,f575,f819,f820,f821,f822,f263,f827,f869,f829,f830,f870,f832,f833,f871,f835,f836,f837,f838,f839,f840,f841,f842,f843,f844,f872,f873,f874,f875,f849,f850,f851,f855,f856,f857,f858,f878,f862,f863,f864,f333,f883,f884,f885,f886,f338,f339,f918,f361,f925,f737,f784,f943,f944,f818,f946,f437,f950,f951,f952,f954,f955,f956,f330,f964,f967,f980,f613,f881,f1021,f1022,f1023,f1024,f942,f1028,f1029,f274,f1090,f1091,f1033,f1092,f1040,f1098,f1042,f1099,f1100,f1045,f1046,f1101,f1048,f1049,f1050,f1051,f1052,f1053,f1054,f1055,f1056,f1057,f1102,f1103,f1104,f1105,f1062,f1063,f1106,f1065,f1107,f1067,f1071,f1072,f1073,f1074,f1075,f1076,f1110,f1080,f1081,f1082,f1084,f945,f1161,f1162,f1167,f1169,f1171,f1177,f1178,f1179,f1183,f1185,f1187,f1147,f1149,f1190,f1158,f1159,f1192,f1195,f1204,f1196,f1123,f1213,f1215,f1212,f1127,f1229,f1230,f1228,f1234,f1235,f1233,f1238,f1239,f1138,f1256,f1258,f1255,f1139,f1267,f1269,f1266,f1163,f1286,f1281,f1282,f1283,f1284,f1285,f1276,f1207,f1293,f1295,f1300,f1301,f1302,f1303,f282,f1304,f1305,f1306,f1307,f1308,f1310,f1311,f1314,f1315,f1317,f1329,f1332,f1333,f1336,f1337,f1348,f1264,f1390,f1275,f1396,f1389,f1395,f1160,f1436,f1440,f1442,f1174,f426,f1449,f1448,f1175,f1176,f1438,f1454,f1457,f1460,f1459,f1208,f1465,f1466,f1224,f1262,f1273,f1456,f1489,f1491,f599,f1613,f1611,f1612,f1027,f1618,f1621,f1622,f1617,f1629,f1633,f1669,f1670,f1671,f1672,f1673,f1674,f1645,f1646,f1675,f1676,f1677,f1678,f1679,f1656,f1657,f1658,f1660,f1661,f1663,f1668,f1654,f1682,f1683,f1647,f1686,f1687,f1648,f1690,f1691,f1630,f1704,f1706,f1643,f1644,f721,f1711,f1718,f1720,f1715,f1716,f1721,f1659,f1722,f1723,f1665,f1666,f1122,f1736,f1738,f264,f1739,f1740,f1744,f1811,f1746,f1747,f1812,f1749,f1750,f1751,f1813,f1753,f1754,f1755,f1756,f1757,f1758,f1759,f1760,f1761,f1762,f1763,f1814,f1815,f1816,f1817,f1768,f1769,f1818,f1771,f1819,f1773,f1779,f1780,f1781,f1782,f1783,f1784,f1822,f1788,f1789,f1790,f1792,f1797,f1826,f1799,f1154,f1155,f1156,f1165,f1850,f1851,f1858,f1856,f1173,f1865,f1862,f1863,f1864,f1181,f1868,f1869,f1884,f1872,f1873,f1874,f1875,f1876,f1877,f1878,f1879,f1880,f1881,f1882,f1883,f1870,f1893,f1894,f1895,f1896,f1897,f1886,f1906,f1907,f1908,f1909,f1910,f1911,f1912,f1867,f1918,f1919,f1920,f1921,f1922,f1923,f1924,f1925,f1913,f283,f1934,f1993,f1936,f1937,f1938,f1939,f1940,f1941,f1942,f1946,f1947,f1948,f1949,f1952,f1953,f1955,f1967,f1970,f1971,f1972,f1975,f1976,f1987,f1916,f1188,f2064,f2065,f2066,f2052,f2073,f2075,f331,f2093,f2095,f2082,f2083,f2084,f2085,f2086,f2087,f2088,f2089,f2090,f2091,f2092,f1439,f2100,f2101,f2102,f1853,f2154,f2155,f2161,f2162,f2147,f2167,f2168,f2151,f2172,f2156,f1861,f2186,f2187,f2181,f2182,f2183,f2184,f2185,f576,f2212,f2219,f2215,f2216,f2217,f2218,f578,f2294,f2301,f2297,f2298,f2299,f2300,f1292,f2392,f2393,f2394,f1885,f2405,f2409,f2411,f1887,f2414,f2427,f2428,f2429,f275,f2433,f2530,f2435,f2531,f2437,f2442,f2532,f2444,f2533,f2534,f2447,f2535,f2449,f2536,f2451,f2452,f2537,f2454,f2455,f2456,f2457,f2458,f2459,f2460,f2461,f2462,f2463,f2538,f2539,f2540,f2541,f2468,f2469,f2542,f2471,f2472,f2543,f2474,f2480,f2481,f2482,f2483,f2484,f2485,f2546,f2492,f2493,f2494,f2497,f2502,f2503,f2504,f2554,f2555,f2507,f2565,f2517,f2520,f2574,f2575,f2523,f2153,f2661,f2662,f2663,f2664,f2180,f2667,f2670,f2671,f2674,f2675,f2676,f2677,f2685,f2679,f2680,f2682,f2683,f2684]) ).
fof(f2684,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(or(strict_implies(X0,X0),strict_implies(X0,X0))) ),
inference(resolution,[],[f2180,f2156]) ).
fof(f2682,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(or(X1,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f2180,f1160]) ).
fof(f2680,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(or(implies(X0,X1),implies(X0,X1))) ),
inference(resolution,[],[f2180,f2153]) ).
fof(f2679,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(possibly(X1),possibly(X1)))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(resolution,[],[f2180,f2052]) ).
fof(f2685,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X1),necessarily(not(X1))))
| is_a_theorem(X0)
| ~ is_a_theorem(necessarily(possibly(X1))) ),
inference(forward_demodulation,[],[f2678,f281]) ).
fof(f2678,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(necessarily(not(X1)),necessarily(not(X1))))
| ~ is_a_theorem(necessarily(possibly(X1))) ),
inference(resolution,[],[f2180,f1887]) ).
fof(f2677,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(necessarily(possibly(X1)),necessarily(possibly(X1))))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(resolution,[],[f2180,f1885]) ).
fof(f2676,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(or(X1,X1),or(X1,X1)))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f2180,f1173]) ).
fof(f2675,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(not(X1),not(X1)))
| ~ is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f2180,f404]) ).
fof(f2674,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(not(X1),not(X1)))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f2180,f1163]) ).
fof(f2671,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(equiv(X1,X0)) ),
inference(resolution,[],[f2180,f1264]) ).
fof(f2670,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f2180,f1275]) ).
fof(f2667,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f2180,f1913]) ).
fof(f2664,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))),
inference(superposition,[],[f2153,f283]) ).
fof(f2663,plain,
! [X2,X0,X1] : is_a_theorem(strict_implies(implies(and(X0,not(X1)),X2),implies(implies(implies(X0,X1),and(X0,not(X1))),X2))),
inference(superposition,[],[f2153,f282]) ).
fof(f2662,plain,
! [X0,X1] : is_a_theorem(strict_implies(implies(necessarily(not(X0)),X1),implies(implies(possibly(X0),necessarily(not(X0))),X1))),
inference(superposition,[],[f2153,f281]) ).
fof(f2661,plain,
! [X0,X1] : is_a_theorem(strict_implies(or(X0,X1),implies(or(not(X0),not(X0)),X1))),
inference(superposition,[],[f2153,f277]) ).
fof(f2523,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(not(or(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(X3,and(not(X0),implies(X1,X2)))) ),
inference(superposition,[],[f1906,f275]) ).
fof(f2575,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(strict_implies(not(X0),and(X1,not(X2))),X3))
| ~ is_a_theorem(necessarily(possibly(and(not(X0),implies(X1,X2))))) ),
inference(forward_demodulation,[],[f2522,f287]) ).
fof(f2522,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(necessarily(or(X0,and(X1,not(X2)))),X3))
| ~ is_a_theorem(necessarily(possibly(and(not(X0),implies(X1,X2))))) ),
inference(superposition,[],[f1887,f275]) ).
fof(f2574,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),and(X1,not(X2))))
| is_a_theorem(strict_implies(and(not(X0),implies(X1,X2)),X3)) ),
inference(forward_demodulation,[],[f2521,f287]) ).
fof(f2521,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f1870,f275]) ).
fof(f2520,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(or(X3,or(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f1867,f275]) ).
fof(f2517,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(or(and(not(X0),implies(X1,X2)),and(X3,or(X0,and(X1,not(X2))))))
| ~ is_a_theorem(necessarily(X3)) ),
inference(superposition,[],[f1439,f275]) ).
fof(f2565,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),and(X1,not(X2)))))
| is_a_theorem(implies(possibly(and(not(X0),implies(X1,X2))),X3)) ),
inference(forward_demodulation,[],[f2514,f287]) ).
fof(f2514,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(or(X0,and(X1,not(X2))))))
| is_a_theorem(implies(possibly(and(not(X0),implies(X1,X2))),X3)) ),
inference(superposition,[],[f1292,f275]) ).
fof(f2507,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(not(or(X0,and(X1,not(X2))))))
| is_a_theorem(or(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f1208,f275]) ).
fof(f2555,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),and(X1,not(X2))))
| is_a_theorem(implies(and(not(X0),implies(X1,X2)),X3)) ),
inference(forward_demodulation,[],[f2506,f287]) ).
fof(f2506,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,and(X1,not(X2)))))
| is_a_theorem(implies(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f1207,f275]) ).
fof(f2554,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),and(X1,not(X2)))))
| is_a_theorem(strict_implies(possibly(and(not(X0),implies(X1,X2))),X3)) ),
inference(forward_demodulation,[],[f2505,f287]) ).
fof(f2505,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(or(X0,and(X1,not(X2))))))
| is_a_theorem(strict_implies(possibly(and(not(X0),implies(X1,X2))),X3)) ),
inference(superposition,[],[f1188,f275]) ).
fof(f2504,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,and(X1,not(X2))),not(X3)))
| is_a_theorem(strict_implies(X3,and(not(X0),implies(X1,X2)))) ),
inference(superposition,[],[f1181,f275]) ).
fof(f2503,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X3),or(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f1181,f275]) ).
fof(f2502,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(or(X0,and(X1,not(X2))),X3))
| ~ is_a_theorem(necessarily(and(not(X0),implies(X1,X2)))) ),
inference(superposition,[],[f1163,f275]) ).
fof(f2497,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(or(X3,not(or(X0,and(X1,not(X2))))))
| is_a_theorem(or(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f881,f275]) ).
fof(f2494,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),and(or(X0,and(X1,not(X2))),or(X0,and(X1,not(X2)))))),
inference(superposition,[],[f755,f275]) ).
fof(f2493,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X3,or(X0,and(X1,not(X2)))),implies(X3,and(not(X0),implies(X1,X2))))),
inference(superposition,[],[f746,f275]) ).
fof(f2492,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),or(X0,and(X1,not(X2))))),
inference(superposition,[],[f742,f275]) ).
fof(f2546,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(not(X0),and(X1,not(X2))),implies(possibly(and(not(X0),implies(X1,X2))),X3))),
inference(forward_demodulation,[],[f2491,f287]) ).
fof(f2491,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(necessarily(or(X0,and(X1,not(X2)))),implies(possibly(and(not(X0),implies(X1,X2))),X3))),
inference(superposition,[],[f653,f275]) ).
fof(f2485,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(X3,or(and(not(X0),implies(X1,X2)),and(not(X3),or(X0,and(X1,not(X2))))))),
inference(superposition,[],[f437,f275]) ).
fof(f2484,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),or(X3,and(or(X0,and(X1,not(X2))),not(X3))))),
inference(superposition,[],[f437,f275]) ).
fof(f2483,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(equiv(or(X0,and(X1,not(X2))),X3))
| is_a_theorem(or(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f410,f275]) ).
fof(f2482,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(equiv(X3,or(X0,and(X1,not(X2)))))
| is_a_theorem(or(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f406,f275]) ).
fof(f2481,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(or(X0,and(X1,not(X2))),X3))
| ~ is_a_theorem(or(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f404,f275]) ).
fof(f2480,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,and(X1,not(X2))),X3))
| is_a_theorem(or(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f402,f275]) ).
fof(f2474,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(not(or(X0,and(X1,not(X2)))))
| is_a_theorem(or(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f350,f275]) ).
fof(f2543,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(not(X0),and(X1,not(X2))),necessarily(not(necessarily(possibly(and(not(X0),implies(X1,X2)))))))),
inference(forward_demodulation,[],[f2473,f287]) ).
fof(f2473,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(or(X0,and(X1,not(X2)))),necessarily(not(necessarily(possibly(and(not(X0),implies(X1,X2)))))))),
inference(superposition,[],[f339,f275]) ).
fof(f2472,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,not(or(X0,and(X1,not(X2))))),or(and(not(X0),implies(X1,X2)),X3))),
inference(superposition,[],[f333,f275]) ).
fof(f2542,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,possibly(and(not(X0),implies(X1,X2)))),implies(strict_implies(not(X0),and(X1,not(X2))),X3))),
inference(forward_demodulation,[],[f2470,f287]) ).
fof(f2470,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,possibly(and(not(X0),implies(X1,X2)))),implies(necessarily(or(X0,and(X1,not(X2)))),X3))),
inference(superposition,[],[f330,f275]) ).
fof(f2469,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(or(X3,or(X0,and(X1,not(X2)))))
| is_a_theorem(implies(and(not(X0),implies(X1,X2)),X3)) ),
inference(superposition,[],[f329,f275]) ).
fof(f2541,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),and(X1,not(X2))),necessarily(possibly(possibly(and(not(X0),implies(X1,X2))))))),
inference(forward_demodulation,[],[f2467,f287]) ).
fof(f2467,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,and(X1,not(X2)))),necessarily(possibly(possibly(and(not(X0),implies(X1,X2))))))),
inference(superposition,[],[f311,f275]) ).
fof(f2540,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(strict_implies(not(X0),and(X1,not(X2))),or(possibly(and(not(X0),implies(X1,X2))),X3))),
inference(forward_demodulation,[],[f2466,f287]) ).
fof(f2466,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(necessarily(or(X0,and(X1,not(X2)))),or(possibly(and(not(X0),implies(X1,X2))),X3))),
inference(superposition,[],[f308,f275]) ).
fof(f2539,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(strict_implies(not(X0),and(X1,not(X2))),or(X3,possibly(and(not(X0),implies(X1,X2)))))),
inference(forward_demodulation,[],[f2465,f287]) ).
fof(f2465,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(necessarily(or(X0,and(X1,not(X2)))),or(X3,possibly(and(not(X0),implies(X1,X2)))))),
inference(superposition,[],[f305,f275]) ).
fof(f2538,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(strict_implies(not(X0),and(X1,not(X2))),implies(X3,possibly(and(not(X0),implies(X1,X2)))))),
inference(forward_demodulation,[],[f2464,f287]) ).
fof(f2464,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(necessarily(or(X0,and(X1,not(X2)))),implies(X3,possibly(and(not(X0),implies(X1,X2)))))),
inference(superposition,[],[f301,f275]) ).
fof(f2463,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),necessarily(possibly(or(X0,and(X1,not(X2))))))),
inference(superposition,[],[f300,f275]) ).
fof(f2462,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),or(or(X0,and(X1,not(X2))),X3))),
inference(superposition,[],[f299,f275]) ).
fof(f2461,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),or(X3,or(X0,and(X1,not(X2)))))),
inference(superposition,[],[f298,f275]) ).
fof(f2460,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(X3,or(and(not(X0),implies(X1,X2)),and(X3,or(X0,and(X1,not(X2))))))),
inference(superposition,[],[f297,f275]) ).
fof(f2459,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(or(and(not(X0),implies(X1,X2)),and(X3,or(X0,and(X1,not(X2))))))
| ~ is_a_theorem(X3) ),
inference(superposition,[],[f296,f275]) ).
fof(f2458,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),implies(X3,and(or(X0,and(X1,not(X2))),X3)))),
inference(superposition,[],[f295,f275]) ).
fof(f2457,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),implies(X3,or(X0,and(X1,not(X2)))))),
inference(superposition,[],[f294,f275]) ).
fof(f2456,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,and(X1,not(X2))),X3),or(and(not(X0),implies(X1,X2)),X3))),
inference(superposition,[],[f292,f275]) ).
fof(f2455,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(equiv(or(X0,and(X1,not(X2))),X3),or(and(not(X0),implies(X1,X2)),X3))),
inference(superposition,[],[f290,f275]) ).
fof(f2454,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(equiv(X3,or(X0,and(X1,not(X2)))),or(and(not(X0),implies(X1,X2)),X3))),
inference(superposition,[],[f289,f275]) ).
fof(f2537,plain,
! [X2,X3,X0,X1,X4] : implies(or(and(not(X0),implies(X1,X2)),X3),X4) = implies(implies(or(X0,and(X1,not(X2))),X3),X4),
inference(forward_demodulation,[],[f2453,f282]) ).
fof(f2453,plain,
! [X2,X3,X0,X1,X4] : implies(or(and(not(X0),implies(X1,X2)),X3),X4) = or(and(or(X0,and(X1,not(X2))),not(X3)),X4),
inference(superposition,[],[f283,f275]) ).
fof(f2452,plain,
! [X2,X3,X0,X1,X4] : implies(or(X3,and(not(X0),implies(X1,X2))),X4) = or(and(not(X3),or(X0,and(X1,not(X2)))),X4),
inference(superposition,[],[f283,f275]) ).
fof(f2451,plain,
! [X2,X3,X0,X1,X4] : implies(implies(X3,and(not(X0),implies(X1,X2))),X4) = or(and(X3,or(X0,and(X1,not(X2)))),X4),
inference(superposition,[],[f282,f275]) ).
fof(f2536,plain,
! [X2,X3,X0,X1] : implies(possibly(and(not(X0),implies(X1,X2))),X3) = or(strict_implies(not(X0),and(X1,not(X2))),X3),
inference(forward_demodulation,[],[f2450,f287]) ).
fof(f2450,plain,
! [X2,X3,X0,X1] : implies(possibly(and(not(X0),implies(X1,X2))),X3) = or(necessarily(or(X0,and(X1,not(X2)))),X3),
inference(superposition,[],[f281,f275]) ).
fof(f2449,plain,
! [X2,X3,X0,X1] : implies(or(X0,and(X1,not(X2))),X3) = or(and(not(X0),implies(X1,X2)),X3),
inference(superposition,[],[f277,f275]) ).
fof(f2535,plain,
! [X2,X3,X0,X1] : or(and(not(X0),implies(X1,X2)),necessarily(not(X3))) = implies(or(X0,and(X1,not(X2))),necessarily(not(X3))),
inference(forward_demodulation,[],[f2448,f263]) ).
fof(f2448,plain,
! [X2,X3,X0,X1] : or(and(not(X0),implies(X1,X2)),necessarily(not(X3))) = not(and(or(X0,and(X1,not(X2))),possibly(X3))),
inference(superposition,[],[f274,f275]) ).
fof(f2447,plain,
! [X2,X3,X0,X1] : not(strict_implies(X3,and(not(X0),implies(X1,X2)))) = possibly(and(X3,or(X0,and(X1,not(X2))))),
inference(superposition,[],[f266,f275]) ).
fof(f2534,plain,
! [X2,X0,X1] : not(necessarily(possibly(and(not(X0),implies(X1,X2))))) = possibly(strict_implies(not(X0),and(X1,not(X2)))),
inference(forward_demodulation,[],[f2446,f287]) ).
fof(f2446,plain,
! [X2,X0,X1] : not(necessarily(possibly(and(not(X0),implies(X1,X2))))) = possibly(necessarily(or(X0,and(X1,not(X2))))),
inference(superposition,[],[f245,f275]) ).
fof(f2533,plain,
! [X2,X3,X0,X1] : implies(or(X0,and(X1,not(X2))),X3) = or(and(not(X0),implies(X1,X2)),X3),
inference(forward_demodulation,[],[f2445,f219]) ).
fof(f2445,plain,
! [X2,X3,X0,X1] : or(and(not(X0),implies(X1,X2)),X3) = not(and(or(X0,and(X1,not(X2))),not(X3))),
inference(superposition,[],[f222,f275]) ).
fof(f2444,plain,
! [X2,X3,X0,X1] : or(X3,and(not(X0),implies(X1,X2))) = not(and(not(X3),or(X0,and(X1,not(X2))))),
inference(superposition,[],[f222,f275]) ).
fof(f2532,plain,
! [X2,X0,X1] : possibly(and(not(X0),implies(X1,X2))) = not(strict_implies(not(X0),and(X1,not(X2)))),
inference(forward_demodulation,[],[f2443,f287]) ).
fof(f2443,plain,
! [X2,X0,X1] : possibly(and(not(X0),implies(X1,X2))) = not(necessarily(or(X0,and(X1,not(X2))))),
inference(superposition,[],[f221,f275]) ).
fof(f2442,plain,
! [X2,X3,X0,X1] : implies(X3,and(not(X0),implies(X1,X2))) = not(and(X3,or(X0,and(X1,not(X2))))),
inference(superposition,[],[f219,f275]) ).
fof(f2437,plain,
! [X2,X0,X1] : or(X2,and(not(X0),not(X1))) = not(and(not(X2),or(X0,X1))),
inference(superposition,[],[f275,f277]) ).
fof(f2531,plain,
! [X2,X3,X0,X1,X4] : or(and(not(X0),implies(X1,X2)),and(X3,not(X4))) = implies(or(X0,and(X1,not(X2))),and(X3,not(X4))),
inference(forward_demodulation,[],[f2436,f264]) ).
fof(f2436,plain,
! [X2,X3,X0,X1,X4] : or(and(not(X0),implies(X1,X2)),and(X3,not(X4))) = not(and(or(X0,and(X1,not(X2))),implies(X3,X4))),
inference(superposition,[],[f275,f275]) ).
fof(f2435,plain,
! [X2,X3,X0,X1,X4] : or(and(X0,implies(X1,X2)),and(X3,not(X4))) = not(and(implies(X0,and(X1,not(X2))),implies(X3,X4))),
inference(superposition,[],[f275,f264]) ).
fof(f2530,plain,
! [X2,X3,X0,X1] : or(and(not(X0),possibly(X1)),and(X2,not(X3))) = implies(or(X0,necessarily(not(X1))),and(X2,not(X3))),
inference(forward_demodulation,[],[f2434,f264]) ).
fof(f2434,plain,
! [X2,X3,X0,X1] : or(and(not(X0),possibly(X1)),and(X2,not(X3))) = not(and(or(X0,necessarily(not(X1))),implies(X2,X3))),
inference(superposition,[],[f275,f274]) ).
fof(f2433,plain,
! [X2,X3,X0,X1] : or(and(X0,possibly(X1)),and(X2,not(X3))) = not(and(implies(X0,necessarily(not(X1))),implies(X2,X3))),
inference(superposition,[],[f275,f263]) ).
fof(f2429,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(strict_implies(X0,and(X1,not(X2))),X3))
| ~ is_a_theorem(necessarily(possibly(and(X0,implies(X1,X2))))) ),
inference(forward_demodulation,[],[f2421,f218]) ).
fof(f2421,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(necessarily(implies(X0,and(X1,not(X2)))),X3))
| ~ is_a_theorem(necessarily(possibly(and(X0,implies(X1,X2))))) ),
inference(superposition,[],[f1887,f264]) ).
fof(f2428,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(strict_implies(not(X0),necessarily(not(X1))),X2))
| ~ is_a_theorem(necessarily(possibly(and(not(X0),possibly(X1))))) ),
inference(forward_demodulation,[],[f2420,f287]) ).
fof(f2420,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(necessarily(or(X0,necessarily(not(X1)))),X2))
| ~ is_a_theorem(necessarily(possibly(and(not(X0),possibly(X1))))) ),
inference(superposition,[],[f1887,f274]) ).
fof(f2427,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(strict_implies(X0,necessarily(not(X1))),X2))
| ~ is_a_theorem(necessarily(possibly(and(X0,possibly(X1))))) ),
inference(forward_demodulation,[],[f2419,f218]) ).
fof(f2419,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(necessarily(implies(X0,necessarily(not(X1)))),X2))
| ~ is_a_theorem(necessarily(possibly(and(X0,possibly(X1))))) ),
inference(superposition,[],[f1887,f263]) ).
fof(f2414,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(resolution,[],[f1887,f261]) ).
fof(f1887,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(possibly(X0))) ),
inference(superposition,[],[f1870,f221]) ).
fof(f2411,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(necessarily(not(strict_implies(X0,X1))),X2)) ),
inference(forward_demodulation,[],[f2410,f218]) ).
fof(f2410,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(strict_implies(necessarily(not(strict_implies(X0,X1))),X2)) ),
inference(forward_demodulation,[],[f2408,f219]) ).
fof(f2408,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(strict_implies(X0,X1))),X2))
| ~ is_a_theorem(necessarily(not(and(X0,not(X1))))) ),
inference(superposition,[],[f1885,f266]) ).
fof(f2409,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(necessarily(possibly(X0)))),X1)) ),
inference(forward_demodulation,[],[f2407,f221]) ).
fof(f2407,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(necessarily(possibly(X0)))),X1))
| ~ is_a_theorem(necessarily(not(necessarily(not(X0))))) ),
inference(superposition,[],[f1885,f245]) ).
fof(f2405,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(implies(necessarily(possibly(X0)),X1)) ),
inference(resolution,[],[f1885,f261]) ).
fof(f1885,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(possibly(X0)),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1870,f338]) ).
fof(f2394,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,and(X1,not(X2)))))
| is_a_theorem(implies(possibly(and(X0,implies(X1,X2))),X3)) ),
inference(forward_demodulation,[],[f2383,f218]) ).
fof(f2383,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(implies(X0,and(X1,not(X2))))))
| is_a_theorem(implies(possibly(and(X0,implies(X1,X2))),X3)) ),
inference(superposition,[],[f1292,f264]) ).
fof(f2393,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),necessarily(not(X1)))))
| is_a_theorem(implies(possibly(and(not(X0),possibly(X1))),X2)) ),
inference(forward_demodulation,[],[f2382,f287]) ).
fof(f2382,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(or(X0,necessarily(not(X1))))))
| is_a_theorem(implies(possibly(and(not(X0),possibly(X1))),X2)) ),
inference(superposition,[],[f1292,f274]) ).
fof(f2392,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,necessarily(not(X1)))))
| is_a_theorem(implies(possibly(and(X0,possibly(X1))),X2)) ),
inference(forward_demodulation,[],[f2381,f218]) ).
fof(f2381,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(implies(X0,necessarily(not(X1))))))
| is_a_theorem(implies(possibly(and(X0,possibly(X1))),X2)) ),
inference(superposition,[],[f1292,f263]) ).
fof(f1292,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(implies(possibly(X0),X1)) ),
inference(superposition,[],[f1276,f281]) ).
fof(f2300,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),implies(X2,X3)),implies(strict_implies(not(X0),X1),strict_implies(X2,X3)))),
inference(superposition,[],[f578,f287]) ).
fof(f2299,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,X1),implies(X2,X3)),implies(strict_implies(X0,X1),strict_implies(X2,X3)))),
inference(superposition,[],[f578,f218]) ).
fof(f2297,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(necessarily(X0),strict_implies(X1,X2)))
| ~ is_a_theorem(strict_implies(X0,implies(X1,X2))) ),
inference(resolution,[],[f578,f242]) ).
fof(f2301,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(necessarily(X0),strict_implies(X1,X2)))
| ~ is_a_theorem(necessarily(strict_implies(X0,implies(X1,X2)))) ),
inference(forward_demodulation,[],[f2295,f218]) ).
fof(f2295,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,implies(X1,X2))))
| is_a_theorem(necessarily(implies(necessarily(X0),strict_implies(X1,X2)))) ),
inference(resolution,[],[f578,f945]) ).
fof(f2294,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(necessarily(X0),strict_implies(X1,X2)))
| ~ is_a_theorem(necessarily(strict_implies(X0,implies(X1,X2)))) ),
inference(resolution,[],[f578,f1617]) ).
fof(f2218,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(implies(X2,X3),or(X0,X1)),implies(strict_implies(X2,X3),strict_implies(not(X0),X1)))),
inference(superposition,[],[f576,f287]) ).
fof(f2215,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(strict_implies(X0,X1),necessarily(X2)))
| ~ is_a_theorem(strict_implies(implies(X0,X1),X2)) ),
inference(resolution,[],[f576,f242]) ).
fof(f2219,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(strict_implies(X0,X1),necessarily(X2)))
| ~ is_a_theorem(necessarily(strict_implies(implies(X0,X1),X2))) ),
inference(forward_demodulation,[],[f2213,f218]) ).
fof(f2213,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(implies(X0,X1),X2)))
| is_a_theorem(necessarily(implies(strict_implies(X0,X1),necessarily(X2)))) ),
inference(resolution,[],[f576,f945]) ).
fof(f2212,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(strict_implies(X0,X1),necessarily(X2)))
| ~ is_a_theorem(necessarily(strict_implies(implies(X0,X1),X2))) ),
inference(resolution,[],[f576,f1617]) ).
fof(f2185,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))
| ~ is_a_theorem(strict_implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1861,f283]) ).
fof(f2184,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(implies(X0,X1),and(X0,not(X1))),X2))
| ~ is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1861,f282]) ).
fof(f2183,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(possibly(X0),necessarily(not(X0))),X1))
| ~ is_a_theorem(strict_implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1861,f281]) ).
fof(f2182,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(or(X0,X0),X1)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(resolution,[],[f1861,f358]) ).
fof(f2181,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(or(X0,X0),X1)))
| is_a_theorem(strict_implies(or(X0,X0),X1)) ),
inference(resolution,[],[f1861,f1853]) ).
fof(f2187,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X0))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f2178,f287]) ).
fof(f2178,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(or(X0,X0)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1861,f945]) ).
fof(f2186,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X0))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1) ),
inference(forward_demodulation,[],[f2177,f287]) ).
fof(f2177,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(necessarily(or(X0,X0))) ),
inference(resolution,[],[f1861,f1617]) ).
fof(f2172,plain,
! [X0] : is_a_theorem(strict_implies(or(X0,not(X0)),equiv(not(X0),not(X0)))),
inference(superposition,[],[f2151,f277]) ).
fof(f2168,plain,
! [X0] : is_a_theorem(strict_implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f2147,f223]) ).
fof(f2167,plain,
! [X0] : is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(superposition,[],[f2147,f220]) ).
fof(f2162,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f2159,f277]) ).
fof(f2159,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,implies(not(X0),X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1853,f277]) ).
fof(f2161,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f2158,f277]) ).
fof(f2158,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1853,f277]) ).
fof(f2155,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,implies(or(X0,X0),X1))) ),
inference(resolution,[],[f1853,f942]) ).
fof(f2154,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[],[f1853,f721]) ).
fof(f2102,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(or(and(X0,implies(X1,X2)),and(X3,implies(X0,and(X1,not(X2))))))
| ~ is_a_theorem(necessarily(X3)) ),
inference(superposition,[],[f1439,f264]) ).
fof(f2101,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(not(X0),possibly(X1)),and(X2,or(X0,necessarily(not(X1))))))
| ~ is_a_theorem(necessarily(X2)) ),
inference(superposition,[],[f1439,f274]) ).
fof(f2100,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,possibly(X1)),and(X2,implies(X0,necessarily(not(X1))))))
| ~ is_a_theorem(necessarily(X2)) ),
inference(superposition,[],[f1439,f263]) ).
fof(f1439,plain,
! [X0,X1] :
( is_a_theorem(or(X1,and(X0,not(X1))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1160,f402]) ).
fof(f2089,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X2,implies(X3,and(not(X0),not(X1)))),implies(and(X3,or(X0,X1)),X2))),
inference(superposition,[],[f331,f222]) ).
fof(f2088,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X2,implies(X3,and(X0,not(X1)))),implies(and(X3,implies(X0,X1)),X2))),
inference(superposition,[],[f331,f219]) ).
fof(f2087,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,implies(X2,necessarily(not(X0)))),implies(and(X2,possibly(X0)),X1))),
inference(superposition,[],[f331,f221]) ).
fof(f2086,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),implies(X2,X3)),implies(and(X2,not(X3)),and(not(X0),not(X1))))),
inference(superposition,[],[f331,f283]) ).
fof(f2083,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,X1)),implies(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f331,f277]) ).
fof(f2082,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(or(X2,implies(X0,X1))) ),
inference(resolution,[],[f331,f242]) ).
fof(f2095,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(and(X1,not(X2)),X0))
| ~ is_a_theorem(strict_implies(not(X0),implies(X1,X2))) ),
inference(forward_demodulation,[],[f2094,f218]) ).
fof(f2094,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),implies(X1,X2)))
| is_a_theorem(necessarily(implies(and(X1,not(X2)),X0))) ),
inference(forward_demodulation,[],[f2080,f287]) ).
fof(f2080,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,implies(X1,X2))))
| is_a_theorem(necessarily(implies(and(X1,not(X2)),X0))) ),
inference(resolution,[],[f331,f945]) ).
fof(f2093,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X2),implies(X0,X1)))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(forward_demodulation,[],[f2079,f287]) ).
fof(f2079,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(necessarily(or(X2,implies(X0,X1)))) ),
inference(resolution,[],[f331,f1617]) ).
fof(f2075,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(not(strict_implies(X0,X1)),X2)) ),
inference(forward_demodulation,[],[f2074,f218]) ).
fof(f2074,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(strict_implies(not(strict_implies(X0,X1)),X2)) ),
inference(forward_demodulation,[],[f2072,f219]) ).
fof(f2072,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(not(strict_implies(X0,X1)),X2))
| ~ is_a_theorem(necessarily(not(and(X0,not(X1))))) ),
inference(superposition,[],[f2052,f266]) ).
fof(f2073,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(strict_implies(not(necessarily(possibly(X0))),X1)) ),
inference(forward_demodulation,[],[f2071,f221]) ).
fof(f2071,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(necessarily(possibly(X0))),X1))
| ~ is_a_theorem(necessarily(not(necessarily(not(X0))))) ),
inference(superposition,[],[f2052,f245]) ).
fof(f2052,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1188,f228]) ).
fof(f2066,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(possibly(and(X0,implies(X1,X2))),X3)) ),
inference(forward_demodulation,[],[f2058,f218]) ).
fof(f2058,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(implies(X0,and(X1,not(X2))))))
| is_a_theorem(strict_implies(possibly(and(X0,implies(X1,X2))),X3)) ),
inference(superposition,[],[f1188,f264]) ).
fof(f2065,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),necessarily(not(X1)))))
| is_a_theorem(strict_implies(possibly(and(not(X0),possibly(X1))),X2)) ),
inference(forward_demodulation,[],[f2057,f287]) ).
fof(f2057,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(or(X0,necessarily(not(X1))))))
| is_a_theorem(strict_implies(possibly(and(not(X0),possibly(X1))),X2)) ),
inference(superposition,[],[f1188,f274]) ).
fof(f2064,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(possibly(and(X0,possibly(X1))),X2)) ),
inference(forward_demodulation,[],[f2056,f218]) ).
fof(f2056,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(implies(X0,necessarily(not(X1))))))
| is_a_theorem(strict_implies(possibly(and(X0,possibly(X1))),X2)) ),
inference(superposition,[],[f1188,f263]) ).
fof(f1188,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(strict_implies(possibly(X0),X1)) ),
inference(forward_demodulation,[],[f1148,f218]) ).
fof(f1148,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(necessarily(implies(possibly(X0),X1))) ),
inference(resolution,[],[f945,f653]) ).
fof(f1916,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1867,f251]) ).
fof(f1987,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),possibly(X2)),implies(necessarily(not(X2)),and(not(X0),not(X1))))),
inference(superposition,[],[f330,f283]) ).
fof(f1976,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),not(not(X2))),or(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f333,f283]) ).
fof(f1975,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),not(not(X2))))
| is_a_theorem(or(X2,and(not(X0),not(X1)))) ),
inference(superposition,[],[f881,f283]) ).
fof(f1972,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),not(X2)),implies(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f316,f283]) ).
fof(f1971,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),not(X2)))
| is_a_theorem(implies(X2,and(not(X0),not(X1)))) ),
inference(superposition,[],[f329,f283]) ).
fof(f1970,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),not(X2)))
| is_a_theorem(strict_implies(X2,and(not(X0),not(X1)))) ),
inference(superposition,[],[f1867,f283]) ).
fof(f1967,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(not(X0),not(X1)))) ),
inference(superposition,[],[f1276,f283]) ).
fof(f1955,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X0),not(X1)))
| is_a_theorem(implies(or(X0,X1),X2)) ),
inference(superposition,[],[f251,f283]) ).
fof(f1949,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))),
inference(superposition,[],[f784,f283]) ).
fof(f1948,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))
| ~ is_a_theorem(implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f942,f283]) ).
fof(f1947,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(or(X0,X1),and(not(X0),not(X1))))
| is_a_theorem(X2)
| ~ is_a_theorem(implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1027,f283]) ).
fof(f1946,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))
| ~ is_a_theorem(strict_implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1173,f283]) ).
fof(f1942,plain,
! [X2,X3,X0,X1,X4] : implies(or(X3,and(X0,implies(X1,X2))),X4) = or(and(not(X3),implies(X0,and(X1,not(X2)))),X4),
inference(superposition,[],[f283,f264]) ).
fof(f1941,plain,
! [X2,X3,X0,X1] : implies(or(X2,and(not(X0),possibly(X1))),X3) = or(and(not(X2),or(X0,necessarily(not(X1)))),X3),
inference(superposition,[],[f283,f274]) ).
fof(f1940,plain,
! [X2,X3,X0,X1] : implies(or(X2,and(X0,possibly(X1))),X3) = or(and(not(X2),implies(X0,necessarily(not(X1)))),X3),
inference(superposition,[],[f283,f263]) ).
fof(f1939,plain,
! [X2,X3,X0,X1] : implies(or(X2,and(not(X0),not(X1))),X3) = or(and(not(X2),or(X0,X1)),X3),
inference(superposition,[],[f283,f222]) ).
fof(f1938,plain,
! [X2,X3,X0,X1] : implies(or(X2,and(X0,not(X1))),X3) = or(and(not(X2),implies(X0,X1)),X3),
inference(superposition,[],[f283,f219]) ).
fof(f1937,plain,
! [X2,X0,X1] : implies(or(X1,necessarily(not(X0))),X2) = or(and(not(X1),possibly(X0)),X2),
inference(superposition,[],[f283,f221]) ).
fof(f1936,plain,
! [X2,X3,X0,X1,X4] : implies(or(and(X0,implies(X1,X2)),X3),X4) = or(and(implies(X0,and(X1,not(X2))),not(X3)),X4),
inference(superposition,[],[f283,f264]) ).
fof(f1993,plain,
! [X2,X3,X0,X1] : implies(or(and(not(X0),possibly(X1)),X2),X3) = implies(implies(or(X0,necessarily(not(X1))),X2),X3),
inference(forward_demodulation,[],[f1935,f282]) ).
fof(f1935,plain,
! [X2,X3,X0,X1] : implies(or(and(not(X0),possibly(X1)),X2),X3) = or(and(or(X0,necessarily(not(X1))),not(X2)),X3),
inference(superposition,[],[f283,f274]) ).
fof(f1934,plain,
! [X2,X3,X0,X1] : implies(or(and(X0,possibly(X1)),X2),X3) = or(and(implies(X0,necessarily(not(X1))),not(X2)),X3),
inference(superposition,[],[f283,f263]) ).
fof(f1925,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),not(X2)))
| is_a_theorem(strict_implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f1867,f282]) ).
fof(f1924,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(X1)))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f1867,f281]) ).
fof(f1923,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(or(X3,implies(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f1867,f264]) ).
fof(f1922,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,or(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f1867,f274]) ).
fof(f1921,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f1867,f263]) ).
fof(f1920,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,or(X0,X1)))
| is_a_theorem(strict_implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1867,f222]) ).
fof(f1919,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,X1)))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1867,f219]) ).
fof(f1918,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1867,f221]) ).
fof(f1912,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(not(implies(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(X3,and(X0,implies(X1,X2)))) ),
inference(superposition,[],[f1906,f264]) ).
fof(f1911,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(or(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(X2,and(not(X0),possibly(X1)))) ),
inference(superposition,[],[f1906,f274]) ).
fof(f1910,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(X2,and(X0,possibly(X1)))) ),
inference(superposition,[],[f1906,f263]) ).
fof(f1909,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(or(X0,X1)))
| is_a_theorem(strict_implies(X2,and(not(X0),not(X1)))) ),
inference(superposition,[],[f1906,f222]) ).
fof(f1908,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,X1)))
| is_a_theorem(strict_implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f1906,f219]) ).
fof(f1907,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,necessarily(not(X0))))
| ~ is_a_theorem(not(possibly(X0))) ),
inference(superposition,[],[f1906,f221]) ).
fof(f1897,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,not(X2))))
| is_a_theorem(strict_implies(and(X0,implies(X1,X2)),X3)) ),
inference(forward_demodulation,[],[f1892,f218]) ).
fof(f1892,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f1870,f264]) ).
fof(f1896,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),necessarily(not(X1))))
| is_a_theorem(strict_implies(and(not(X0),possibly(X1)),X2)) ),
inference(forward_demodulation,[],[f1891,f287]) ).
fof(f1891,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f1870,f274]) ).
fof(f1895,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,necessarily(not(X1))))
| is_a_theorem(strict_implies(and(X0,possibly(X1)),X2)) ),
inference(forward_demodulation,[],[f1890,f218]) ).
fof(f1890,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f1870,f263]) ).
fof(f1894,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| is_a_theorem(strict_implies(and(not(X0),not(X1)),X2)) ),
inference(forward_demodulation,[],[f1889,f287]) ).
fof(f1889,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| is_a_theorem(strict_implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1870,f222]) ).
fof(f1893,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(forward_demodulation,[],[f1888,f218]) ).
fof(f1888,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1870,f219]) ).
fof(f1883,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X3),implies(X0,and(X1,not(X2)))))
| is_a_theorem(strict_implies(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f1181,f264]) ).
fof(f1882,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X2),or(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f1181,f274]) ).
fof(f1881,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X2),implies(X0,necessarily(not(X1)))))
| is_a_theorem(strict_implies(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f1181,f263]) ).
fof(f1880,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X2),or(X0,X1)))
| is_a_theorem(strict_implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1181,f222]) ).
fof(f1879,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X2),implies(X0,X1)))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1181,f219]) ).
fof(f1878,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1181,f221]) ).
fof(f1877,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,and(X1,not(X2))),not(X3)))
| is_a_theorem(strict_implies(X3,and(X0,implies(X1,X2)))) ),
inference(superposition,[],[f1181,f264]) ).
fof(f1876,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,necessarily(not(X1))),not(X2)))
| is_a_theorem(strict_implies(X2,and(not(X0),possibly(X1)))) ),
inference(superposition,[],[f1181,f274]) ).
fof(f1875,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,necessarily(not(X1))),not(X2)))
| is_a_theorem(strict_implies(X2,and(X0,possibly(X1)))) ),
inference(superposition,[],[f1181,f263]) ).
fof(f1874,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,X1),not(X2)))
| is_a_theorem(strict_implies(X2,and(not(X0),not(X1)))) ),
inference(superposition,[],[f1181,f222]) ).
fof(f1873,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),not(X2)))
| is_a_theorem(strict_implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f1181,f219]) ).
fof(f1872,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(X0),not(X1)))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f1181,f221]) ).
fof(f1884,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1871,f277]) ).
fof(f1871,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(not(X1),not(X0))) ),
inference(resolution,[],[f1181,f247]) ).
fof(f1869,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X1),not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1181,f1264]) ).
fof(f1868,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),not(X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1181,f1275]) ).
fof(f1864,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(implies(X0,X1),and(X0,not(X1))),X2))
| ~ is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1173,f282]) ).
fof(f1863,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(possibly(X0),necessarily(not(X0))),X1))
| ~ is_a_theorem(strict_implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1173,f281]) ).
fof(f1862,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(or(X0,X0),X1)))
| is_a_theorem(strict_implies(or(X0,X0),X1)) ),
inference(resolution,[],[f1173,f1165]) ).
fof(f1865,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X0))
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f1859,f287]) ).
fof(f1859,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(or(X0,X0))) ),
inference(resolution,[],[f1173,f818]) ).
fof(f1856,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1165,f277]) ).
fof(f1858,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f1855,f277]) ).
fof(f1855,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(or(X0,implies(not(X0),X1))) ),
inference(resolution,[],[f1165,f404]) ).
fof(f1851,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1165,f1264]) ).
fof(f1850,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(implies(X0,X1),X0))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1165,f1275]) ).
fof(f1155,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(resolution,[],[f945,f424]) ).
fof(f1154,plain,
! [X0] :
( is_a_theorem(necessarily(strict_equiv(X0,X0)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X0))) ),
inference(resolution,[],[f945,f753]) ).
fof(f1799,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(not(implies(X0,and(X1,not(X2))))))
| is_a_theorem(or(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f1208,f264]) ).
fof(f1826,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,and(X1,not(X2))))
| is_a_theorem(implies(and(X0,implies(X1,X2)),X3)) ),
inference(forward_demodulation,[],[f1798,f218]) ).
fof(f1798,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,and(X1,not(X2)))))
| is_a_theorem(implies(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f1207,f264]) ).
fof(f1797,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,and(X1,not(X2))),X3))
| ~ is_a_theorem(necessarily(and(X0,implies(X1,X2)))) ),
inference(superposition,[],[f1163,f264]) ).
fof(f1792,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(or(X3,not(implies(X0,and(X1,not(X2))))))
| is_a_theorem(or(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f881,f264]) ).
fof(f1790,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),and(implies(X0,and(X1,not(X2))),implies(X0,and(X1,not(X2)))))),
inference(superposition,[],[f755,f264]) ).
fof(f1789,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X3,implies(X0,and(X1,not(X2)))),implies(X3,and(X0,implies(X1,X2))))),
inference(superposition,[],[f746,f264]) ).
fof(f1788,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f742,f264]) ).
fof(f1822,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(X0,and(X1,not(X2))),implies(possibly(and(X0,implies(X1,X2))),X3))),
inference(forward_demodulation,[],[f1787,f218]) ).
fof(f1787,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(necessarily(implies(X0,and(X1,not(X2)))),implies(possibly(and(X0,implies(X1,X2))),X3))),
inference(superposition,[],[f653,f264]) ).
fof(f1784,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(X3,or(and(X0,implies(X1,X2)),and(not(X3),implies(X0,and(X1,not(X2))))))),
inference(superposition,[],[f437,f264]) ).
fof(f1783,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),or(X3,and(implies(X0,and(X1,not(X2))),not(X3))))),
inference(superposition,[],[f437,f264]) ).
fof(f1782,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(equiv(implies(X0,and(X1,not(X2))),X3))
| is_a_theorem(or(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f410,f264]) ).
fof(f1781,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(equiv(X3,implies(X0,and(X1,not(X2)))))
| is_a_theorem(or(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f406,f264]) ).
fof(f1780,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,and(X1,not(X2))),X3))
| ~ is_a_theorem(or(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f404,f264]) ).
fof(f1779,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,and(X1,not(X2))),X3))
| is_a_theorem(or(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f402,f264]) ).
fof(f1773,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(not(implies(X0,and(X1,not(X2)))))
| is_a_theorem(or(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f350,f264]) ).
fof(f1819,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X0,and(X1,not(X2))),necessarily(not(necessarily(possibly(and(X0,implies(X1,X2)))))))),
inference(forward_demodulation,[],[f1772,f218]) ).
fof(f1772,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(implies(X0,and(X1,not(X2)))),necessarily(not(necessarily(possibly(and(X0,implies(X1,X2)))))))),
inference(superposition,[],[f339,f264]) ).
fof(f1771,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(or(X3,not(implies(X0,and(X1,not(X2))))),or(and(X0,implies(X1,X2)),X3))),
inference(superposition,[],[f333,f264]) ).
fof(f1769,plain,
! [X2,X3,X0,X1] :
( ~ is_a_theorem(or(X3,implies(X0,and(X1,not(X2)))))
| is_a_theorem(implies(and(X0,implies(X1,X2)),X3)) ),
inference(superposition,[],[f329,f264]) ).
fof(f1817,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,and(X1,not(X2))),necessarily(possibly(possibly(and(X0,implies(X1,X2))))))),
inference(forward_demodulation,[],[f1767,f218]) ).
fof(f1767,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,and(X1,not(X2)))),necessarily(possibly(possibly(and(X0,implies(X1,X2))))))),
inference(superposition,[],[f311,f264]) ).
fof(f1816,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(strict_implies(X0,and(X1,not(X2))),or(possibly(and(X0,implies(X1,X2))),X3))),
inference(forward_demodulation,[],[f1766,f218]) ).
fof(f1766,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(necessarily(implies(X0,and(X1,not(X2)))),or(possibly(and(X0,implies(X1,X2))),X3))),
inference(superposition,[],[f308,f264]) ).
fof(f1815,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(strict_implies(X0,and(X1,not(X2))),or(X3,possibly(and(X0,implies(X1,X2)))))),
inference(forward_demodulation,[],[f1765,f218]) ).
fof(f1765,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(necessarily(implies(X0,and(X1,not(X2)))),or(X3,possibly(and(X0,implies(X1,X2)))))),
inference(superposition,[],[f305,f264]) ).
fof(f1814,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(strict_implies(X0,and(X1,not(X2))),implies(X3,possibly(and(X0,implies(X1,X2)))))),
inference(forward_demodulation,[],[f1764,f218]) ).
fof(f1764,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(necessarily(implies(X0,and(X1,not(X2)))),implies(X3,possibly(and(X0,implies(X1,X2)))))),
inference(superposition,[],[f301,f264]) ).
fof(f1763,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),necessarily(possibly(implies(X0,and(X1,not(X2))))))),
inference(superposition,[],[f300,f264]) ).
fof(f1762,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),or(implies(X0,and(X1,not(X2))),X3))),
inference(superposition,[],[f299,f264]) ).
fof(f1761,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),or(X3,implies(X0,and(X1,not(X2)))))),
inference(superposition,[],[f298,f264]) ).
fof(f1760,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(X3,or(and(X0,implies(X1,X2)),and(X3,implies(X0,and(X1,not(X2))))))),
inference(superposition,[],[f297,f264]) ).
fof(f1759,plain,
! [X2,X3,X0,X1] :
( is_a_theorem(or(and(X0,implies(X1,X2)),and(X3,implies(X0,and(X1,not(X2))))))
| ~ is_a_theorem(X3) ),
inference(superposition,[],[f296,f264]) ).
fof(f1758,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),implies(X3,and(implies(X0,and(X1,not(X2))),X3)))),
inference(superposition,[],[f295,f264]) ).
fof(f1757,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),implies(X3,implies(X0,and(X1,not(X2)))))),
inference(superposition,[],[f294,f264]) ).
fof(f1756,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,and(X1,not(X2))),X3),or(and(X0,implies(X1,X2)),X3))),
inference(superposition,[],[f292,f264]) ).
fof(f1755,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(equiv(implies(X0,and(X1,not(X2))),X3),or(and(X0,implies(X1,X2)),X3))),
inference(superposition,[],[f290,f264]) ).
fof(f1754,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(equiv(X3,implies(X0,and(X1,not(X2)))),or(and(X0,implies(X1,X2)),X3))),
inference(superposition,[],[f289,f264]) ).
fof(f1753,plain,
! [X2,X3,X0,X1,X4] : implies(implies(X3,and(X0,implies(X1,X2))),X4) = or(and(X3,implies(X0,and(X1,not(X2)))),X4),
inference(superposition,[],[f282,f264]) ).
fof(f1813,plain,
! [X2,X3,X0,X1] : implies(possibly(and(X0,implies(X1,X2))),X3) = or(strict_implies(X0,and(X1,not(X2))),X3),
inference(forward_demodulation,[],[f1752,f218]) ).
fof(f1752,plain,
! [X2,X3,X0,X1] : implies(possibly(and(X0,implies(X1,X2))),X3) = or(necessarily(implies(X0,and(X1,not(X2)))),X3),
inference(superposition,[],[f281,f264]) ).
fof(f1751,plain,
! [X2,X3,X0,X1] : implies(implies(X0,and(X1,not(X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(superposition,[],[f277,f264]) ).
fof(f1750,plain,
! [X2,X3,X0,X1] : or(and(X0,implies(X1,X2)),necessarily(not(X3))) = not(and(implies(X0,and(X1,not(X2))),possibly(X3))),
inference(superposition,[],[f274,f264]) ).
fof(f1749,plain,
! [X2,X3,X0,X1] : not(strict_implies(X3,and(X0,implies(X1,X2)))) = possibly(and(X3,implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f266,f264]) ).
fof(f1812,plain,
! [X2,X0,X1] : not(necessarily(possibly(and(X0,implies(X1,X2))))) = possibly(strict_implies(X0,and(X1,not(X2)))),
inference(forward_demodulation,[],[f1748,f218]) ).
fof(f1748,plain,
! [X2,X0,X1] : not(necessarily(possibly(and(X0,implies(X1,X2))))) = possibly(necessarily(implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f245,f264]) ).
fof(f1747,plain,
! [X2,X3,X0,X1] : or(and(X0,implies(X1,X2)),X3) = not(and(implies(X0,and(X1,not(X2))),not(X3))),
inference(superposition,[],[f222,f264]) ).
fof(f1746,plain,
! [X2,X3,X0,X1] : or(X3,and(X0,implies(X1,X2))) = not(and(not(X3),implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f222,f264]) ).
fof(f1811,plain,
! [X2,X0,X1] : not(strict_implies(X0,and(X1,not(X2)))) = possibly(and(X0,implies(X1,X2))),
inference(forward_demodulation,[],[f1745,f218]) ).
fof(f1745,plain,
! [X2,X0,X1] : possibly(and(X0,implies(X1,X2))) = not(necessarily(implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f221,f264]) ).
fof(f1744,plain,
! [X2,X3,X0,X1] : implies(X3,and(X0,implies(X1,X2))) = not(and(X3,implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f219,f264]) ).
fof(f1739,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
inference(superposition,[],[f264,f277]) ).
fof(f1738,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| is_a_theorem(necessarily(equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1737,f218]) ).
fof(f1737,plain,
! [X0,X1] :
( is_a_theorem(necessarily(equiv(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1122,f223]) ).
fof(f1736,plain,
! [X0,X1] :
( is_a_theorem(necessarily(strict_equiv(X0,X1)))
| ~ is_a_theorem(necessarily(strict_implies(X1,X0)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f1122,f220]) ).
fof(f1122,plain,
! [X0,X1] :
( is_a_theorem(necessarily(and(X1,X0)))
| ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f945,f253]) ).
fof(f1666,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X1,X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1617,f425]) ).
fof(f1665,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1617,f424]) ).
fof(f1723,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1659,f1262]) ).
fof(f1722,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X1,X0))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1659,f1273]) ).
fof(f1659,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1617,f248]) ).
fof(f1721,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),or(X0,X1)))
| ~ is_a_theorem(or(X0,X2)) ),
inference(forward_demodulation,[],[f1717,f277]) ).
fof(f1717,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),or(X0,X1)))
| ~ is_a_theorem(implies(not(X0),X2)) ),
inference(superposition,[],[f721,f277]) ).
fof(f1716,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,not(X0))) ),
inference(superposition,[],[f721,f277]) ).
fof(f1720,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(X0,X2))
| ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1719,f218]) ).
fof(f1719,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(implies(X0,X2))) ),
inference(forward_demodulation,[],[f1713,f218]) ).
fof(f1713,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(implies(X1,X2)))
| is_a_theorem(necessarily(implies(X0,X2))) ),
inference(resolution,[],[f721,f945]) ).
fof(f1718,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(forward_demodulation,[],[f1712,f218]) ).
fof(f1712,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(necessarily(implies(X1,X2))) ),
inference(resolution,[],[f721,f1617]) ).
fof(f1644,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1617,f236]) ).
fof(f1643,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X1,X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1617,f235]) ).
fof(f1706,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1705,f218]) ).
fof(f1705,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1630,f223]) ).
fof(f1704,plain,
! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
| ~ is_a_theorem(necessarily(strict_implies(X1,X0)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f1630,f220]) ).
fof(f1630,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1617,f253]) ).
fof(f1691,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f1648,f223]) ).
fof(f1690,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f1648,f220]) ).
fof(f1648,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X1,X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1617,f233]) ).
fof(f1687,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1647,f223]) ).
fof(f1686,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f1647,f220]) ).
fof(f1647,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1617,f232]) ).
fof(f1683,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f1654,f287]) ).
fof(f1682,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1654,f218]) ).
fof(f1654,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1617,f225]) ).
fof(f1663,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1617,f292]) ).
fof(f1661,plain,
! [X0,X1] :
( is_a_theorem(implies(strict_implies(X0,X1),strict_equiv(X1,X0)))
| ~ is_a_theorem(necessarily(strict_implies(X1,X0))) ),
inference(resolution,[],[f1617,f426]) ).
fof(f1660,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(resolution,[],[f1617,f529]) ).
fof(f1658,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(resolution,[],[f1617,f339]) ).
fof(f1657,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(resolution,[],[f1617,f653]) ).
fof(f1656,plain,
! [X0,X1] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(necessarily(X1)))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f1617,f575]) ).
fof(f1679,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),possibly(X0)))
| is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(forward_demodulation,[],[f1653,f287]) ).
fof(f1653,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(or(X1,possibly(X0)))) ),
inference(resolution,[],[f1617,f330]) ).
fof(f1678,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f1652,f287]) ).
fof(f1652,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(or(X0,or(X0,X1)))) ),
inference(resolution,[],[f1617,f361]) ).
fof(f1677,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f1651,f287]) ).
fof(f1651,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(or(X1,not(not(X0))))) ),
inference(resolution,[],[f1617,f333]) ).
fof(f1675,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),X1))
| is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1649,f287]) ).
fof(f1649,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(or(X1,X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f1617,f942]) ).
fof(f1646,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1617,f290]) ).
fof(f1645,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X1,not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1617,f289]) ).
fof(f1674,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1642,f218]) ).
fof(f1642,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1617,f599]) ).
fof(f1673,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(forward_demodulation,[],[f1640,f218]) ).
fof(f1640,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f1617,f784]) ).
fof(f1672,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,X1))
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),X1))) ),
inference(forward_demodulation,[],[f1639,f218]) ).
fof(f1639,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),X1)))
| ~ is_a_theorem(necessarily(implies(X2,X1))) ),
inference(resolution,[],[f1617,f244]) ).
fof(f1671,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,X0))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) ),
inference(forward_demodulation,[],[f1638,f218]) ).
fof(f1638,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(necessarily(implies(X2,X0))) ),
inference(resolution,[],[f1617,f243]) ).
fof(f1670,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| is_a_theorem(implies(implies(X0,X1),equiv(X1,X0))) ),
inference(forward_demodulation,[],[f1637,f218]) ).
fof(f1637,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
| ~ is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f1617,f240]) ).
fof(f1669,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1636,f218]) ).
fof(f1636,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(implies(X0,implies(X0,X1)))) ),
inference(resolution,[],[f1617,f238]) ).
fof(f1633,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1617,f297]) ).
fof(f1629,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1617,f1438]) ).
fof(f1622,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),and(X0,not(X1))))
| is_a_theorem(X2)
| ~ is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1027,f282]) ).
fof(f1621,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),necessarily(not(X0))))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1027,f281]) ).
fof(f1618,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1027,f1196]) ).
fof(f1612,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),equiv(X1,not(X0))))
| ~ is_a_theorem(implies(X1,not(X0))) ),
inference(superposition,[],[f599,f277]) ).
fof(f1613,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1609,f218]) ).
fof(f1609,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(implies(X1,X0)))
| is_a_theorem(necessarily(equiv(X0,X1))) ),
inference(resolution,[],[f599,f945]) ).
fof(f1491,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1490,f218]) ).
fof(f1490,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f1456,f223]) ).
fof(f1489,plain,
! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f1456,f220]) ).
fof(f1273,plain,
! [X0,X1] :
( is_a_theorem(necessarily(strict_implies(X1,X0)))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(superposition,[],[f1266,f220]) ).
fof(f1262,plain,
! [X0,X1] :
( is_a_theorem(necessarily(strict_implies(X0,X1)))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(superposition,[],[f1255,f220]) ).
fof(f1224,plain,
! [X0] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X0)))
| is_a_theorem(strict_equiv(X0,X0)) ),
inference(superposition,[],[f1212,f220]) ).
fof(f1466,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(not(or(X0,necessarily(not(X1))))))
| is_a_theorem(or(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f1208,f274]) ).
fof(f1465,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(not(implies(X0,necessarily(not(X1))))))
| is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f1208,f263]) ).
fof(f1208,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1196,f881]) ).
fof(f1459,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f1438,f277]) ).
fof(f1460,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1458,f218]) ).
fof(f1458,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1438,f223]) ).
fof(f1457,plain,
! [X0,X1] :
( is_a_theorem(implies(strict_implies(X1,X0),strict_equiv(X0,X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(superposition,[],[f1438,f220]) ).
fof(f1454,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(necessarily(and(X0,X1))) ),
inference(resolution,[],[f1438,f945]) ).
fof(f1176,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1135,f218]) ).
fof(f1135,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f945,f236]) ).
fof(f1175,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(forward_demodulation,[],[f1134,f218]) ).
fof(f1134,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f945,f235]) ).
fof(f1448,plain,
! [X0,X1] :
( is_a_theorem(implies(strict_implies(X0,X1),strict_equiv(X1,X0)))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f426,f242]) ).
fof(f1449,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(strict_implies(X1,X0),strict_equiv(X0,X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(forward_demodulation,[],[f1446,f218]) ).
fof(f1446,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(necessarily(implies(strict_implies(X1,X0),strict_equiv(X0,X1)))) ),
inference(resolution,[],[f426,f945]) ).
fof(f1174,plain,
! [X0] :
( is_a_theorem(necessarily(equiv(X0,X0)))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(forward_demodulation,[],[f1133,f218]) ).
fof(f1133,plain,
! [X0] :
( ~ is_a_theorem(necessarily(implies(X0,X0)))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(resolution,[],[f945,f731]) ).
fof(f1442,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1441,f218]) ).
fof(f1441,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1160,f223]) ).
fof(f1440,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(strict_implies(X1,X0),strict_equiv(X0,X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(superposition,[],[f1160,f220]) ).
fof(f1436,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(and(X0,X1)))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1160,f818]) ).
fof(f1395,plain,
~ is_a_theorem(equiv(and(sK1,sK0),and(sK0,sK1))),
inference(resolution,[],[f1275,f224]) ).
fof(f1389,plain,
~ is_a_theorem(equiv(and(sK0,sK1),and(sK1,sK0))),
inference(resolution,[],[f1264,f224]) ).
fof(f1396,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1275,f818]) ).
fof(f1275,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(forward_demodulation,[],[f1274,f218]) ).
fof(f1274,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(superposition,[],[f1266,f223]) ).
fof(f1390,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1264,f818]) ).
fof(f1264,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(forward_demodulation,[],[f1263,f218]) ).
fof(f1263,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1255,f223]) ).
fof(f1337,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),not(not(X2))),or(X2,and(X0,not(X1))))),
inference(superposition,[],[f333,f282]) ).
fof(f1336,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),not(not(X2))))
| is_a_theorem(or(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f881,f282]) ).
fof(f1329,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1276,f282]) ).
fof(f1317,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f251,f282]) ).
fof(f1311,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(and(X0,not(X1)),X2),implies(implies(implies(X0,X1),and(X0,not(X1))),X2))),
inference(superposition,[],[f784,f282]) ).
fof(f1310,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(implies(X0,X1),and(X0,not(X1))),X2))
| ~ is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f942,f282]) ).
fof(f1308,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(not(X0),possibly(X1))),X3) = or(and(X2,or(X0,necessarily(not(X1)))),X3),
inference(superposition,[],[f282,f274]) ).
fof(f1307,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(X0,possibly(X1))),X3) = or(and(X2,implies(X0,necessarily(not(X1)))),X3),
inference(superposition,[],[f282,f263]) ).
fof(f1306,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(not(X0),not(X1))),X3) = or(and(X2,or(X0,X1)),X3),
inference(superposition,[],[f282,f222]) ).
fof(f1305,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(X0,not(X1))),X3) = or(and(X2,implies(X0,X1)),X3),
inference(superposition,[],[f282,f219]) ).
fof(f1304,plain,
! [X2,X0,X1] : implies(implies(X1,necessarily(not(X0))),X2) = or(and(X1,possibly(X0)),X2),
inference(superposition,[],[f282,f221]) ).
fof(f1303,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),necessarily(not(X1))))
| is_a_theorem(implies(and(not(X0),possibly(X1)),X2)) ),
inference(forward_demodulation,[],[f1299,f287]) ).
fof(f1299,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,necessarily(not(X1)))))
| is_a_theorem(implies(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f1207,f274]) ).
fof(f1302,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,necessarily(not(X1))))
| is_a_theorem(implies(and(X0,possibly(X1)),X2)) ),
inference(forward_demodulation,[],[f1298,f218]) ).
fof(f1298,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,necessarily(not(X1)))))
| is_a_theorem(implies(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f1207,f263]) ).
fof(f1301,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| is_a_theorem(implies(and(not(X0),not(X1)),X2)) ),
inference(forward_demodulation,[],[f1297,f287]) ).
fof(f1297,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| is_a_theorem(implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1207,f222]) ).
fof(f1300,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(forward_demodulation,[],[f1296,f218]) ).
fof(f1296,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1207,f219]) ).
fof(f1295,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(possibly(X0))) ),
inference(superposition,[],[f1207,f221]) ).
fof(f1293,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(possibly(X0)),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1207,f338]) ).
fof(f1207,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1196,f329]) ).
fof(f1285,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(or(X0,necessarily(not(X1))),X2))
| ~ is_a_theorem(necessarily(and(not(X0),possibly(X1)))) ),
inference(superposition,[],[f1163,f274]) ).
fof(f1284,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,necessarily(not(X1))),X2))
| ~ is_a_theorem(necessarily(and(X0,possibly(X1)))) ),
inference(superposition,[],[f1163,f263]) ).
fof(f1283,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(or(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(not(X0),not(X1)))) ),
inference(superposition,[],[f1163,f222]) ).
fof(f1282,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1163,f219]) ).
fof(f1281,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1163,f221]) ).
fof(f1286,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1280,f277]) ).
fof(f1280,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[],[f1163,f261]) ).
fof(f1266,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X1,X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1139,f228]) ).
fof(f1269,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1268,f218]) ).
fof(f1268,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(superposition,[],[f1139,f223]) ).
fof(f1267,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X1,X0))) ),
inference(superposition,[],[f1139,f220]) ).
fof(f1139,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f945,f233]) ).
fof(f1255,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1138,f228]) ).
fof(f1258,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1257,f218]) ).
fof(f1257,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1138,f223]) ).
fof(f1256,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(superposition,[],[f1138,f220]) ).
fof(f1138,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f945,f232]) ).
fof(f1239,plain,
! [X0,X1] :
( is_a_theorem(not(strict_implies(X0,X1)))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1233,f266]) ).
fof(f1238,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(not(necessarily(possibly(X0)))) ),
inference(superposition,[],[f1233,f245]) ).
fof(f1233,plain,
! [X0] :
( is_a_theorem(possibly(X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1228,f258]) ).
fof(f1235,plain,
! [X0,X1] :
( is_a_theorem(necessarily(not(strict_implies(X0,X1))))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1228,f266]) ).
fof(f1234,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1228,f245]) ).
fof(f1228,plain,
! [X0] :
( is_a_theorem(necessarily(possibly(X0)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1127,f258]) ).
fof(f1230,plain,
! [X0,X1] :
( is_a_theorem(necessarily(necessarily(not(strict_implies(X0,X1)))))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1127,f266]) ).
fof(f1229,plain,
! [X0] :
( is_a_theorem(necessarily(necessarily(not(necessarily(possibly(X0))))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1127,f245]) ).
fof(f1127,plain,
! [X0] :
( is_a_theorem(necessarily(necessarily(possibly(X0))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f945,f226]) ).
fof(f1212,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1123,f258]) ).
fof(f1215,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(forward_demodulation,[],[f1214,f218]) ).
fof(f1214,plain,
! [X0] :
( is_a_theorem(necessarily(equiv(X0,X0)))
| ~ is_a_theorem(necessarily(implies(X0,X0))) ),
inference(superposition,[],[f1123,f223]) ).
fof(f1213,plain,
! [X0] :
( is_a_theorem(necessarily(strict_equiv(X0,X0)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X0))) ),
inference(superposition,[],[f1123,f220]) ).
fof(f1123,plain,
! [X0] :
( is_a_theorem(necessarily(and(X0,X0)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f945,f728]) ).
fof(f1204,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f1195,f277]) ).
fof(f1192,plain,
~ is_a_theorem(necessarily(and(sK1,sK0))),
inference(resolution,[],[f1159,f224]) ).
fof(f1158,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f945,f277]) ).
fof(f1190,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(forward_demodulation,[],[f1151,f218]) ).
fof(f1151,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(necessarily(implies(necessarily(X0),necessarily(X1)))) ),
inference(resolution,[],[f945,f529]) ).
fof(f1149,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(necessarily(necessarily(not(necessarily(possibly(X0)))))) ),
inference(resolution,[],[f945,f339]) ).
fof(f1147,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(necessarily(necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f945,f575]) ).
fof(f1187,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(X1)),X0))
| ~ is_a_theorem(strict_implies(not(X0),possibly(X1))) ),
inference(forward_demodulation,[],[f1186,f218]) ).
fof(f1186,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),possibly(X1)))
| is_a_theorem(necessarily(implies(necessarily(not(X1)),X0))) ),
inference(forward_demodulation,[],[f1144,f287]) ).
fof(f1144,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,possibly(X1))))
| is_a_theorem(necessarily(implies(necessarily(not(X1)),X0))) ),
inference(resolution,[],[f945,f330]) ).
fof(f1185,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(strict_implies(not(X0),or(X0,X1))) ),
inference(forward_demodulation,[],[f1184,f287]) ).
fof(f1184,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(forward_demodulation,[],[f1143,f287]) ).
fof(f1143,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,or(X0,X1))))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f945,f361]) ).
fof(f1183,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(strict_implies(not(X0),not(not(X1)))) ),
inference(forward_demodulation,[],[f1182,f287]) ).
fof(f1182,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(not(X1))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(forward_demodulation,[],[f1142,f287]) ).
fof(f1142,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,not(not(X1)))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f945,f333]) ).
fof(f1179,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X0))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1140,f287]) ).
fof(f1140,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X0)))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f945,f942]) ).
fof(f1178,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(necessarily(equiv(not(X0),X1))) ),
inference(forward_demodulation,[],[f1137,f287]) ).
fof(f1137,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(not(X0),X1)))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f945,f290]) ).
fof(f1177,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(necessarily(equiv(X0,not(X1)))) ),
inference(forward_demodulation,[],[f1136,f287]) ).
fof(f1136,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,not(X1))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f945,f289]) ).
fof(f1171,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1170,f218]) ).
fof(f1170,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
inference(forward_demodulation,[],[f1131,f218]) ).
fof(f1131,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
inference(resolution,[],[f945,f244]) ).
fof(f1169,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1168,f218]) ).
fof(f1168,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(implies(implies(X1,X2),implies(X0,X2)))) ),
inference(forward_demodulation,[],[f1130,f218]) ).
fof(f1130,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(implies(X1,X2),implies(X0,X2)))) ),
inference(resolution,[],[f945,f243]) ).
fof(f1167,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1166,f218]) ).
fof(f1166,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(forward_demodulation,[],[f1129,f218]) ).
fof(f1129,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(resolution,[],[f945,f240]) ).
fof(f1162,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),and(X0,not(X1))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1125,f287]) ).
fof(f1125,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X1,and(X0,not(X1))))) ),
inference(resolution,[],[f945,f297]) ).
fof(f1161,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1124,f287]) ).
fof(f1124,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f945,f229]) ).
fof(f1084,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,not(or(X0,necessarily(not(X1))))))
| is_a_theorem(or(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f881,f274]) ).
fof(f1082,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),and(or(X0,necessarily(not(X1))),or(X0,necessarily(not(X1)))))),
inference(superposition,[],[f755,f274]) ).
fof(f1081,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,or(X0,necessarily(not(X1)))),implies(X2,and(not(X0),possibly(X1))))),
inference(superposition,[],[f746,f274]) ).
fof(f1080,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(X0,necessarily(not(X1))))),
inference(superposition,[],[f742,f274]) ).
fof(f1110,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(not(X0),necessarily(not(X1))),implies(possibly(and(not(X0),possibly(X1))),X2))),
inference(forward_demodulation,[],[f1079,f287]) ).
fof(f1079,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(or(X0,necessarily(not(X1)))),implies(possibly(and(not(X0),possibly(X1))),X2))),
inference(superposition,[],[f653,f274]) ).
fof(f1076,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(not(X0),possibly(X1)),and(not(X2),or(X0,necessarily(not(X1))))))),
inference(superposition,[],[f437,f274]) ).
fof(f1075,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(X2,and(or(X0,necessarily(not(X1))),not(X2))))),
inference(superposition,[],[f437,f274]) ).
fof(f1074,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(or(X0,necessarily(not(X1))),X2))
| is_a_theorem(or(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f410,f274]) ).
fof(f1073,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X2,or(X0,necessarily(not(X1)))))
| is_a_theorem(or(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f406,f274]) ).
fof(f1072,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(or(X0,necessarily(not(X1))),X2))
| ~ is_a_theorem(or(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f404,f274]) ).
fof(f1071,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,necessarily(not(X1))),X2))
| is_a_theorem(or(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f402,f274]) ).
fof(f1067,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(or(X0,necessarily(not(X1)))))
| is_a_theorem(or(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f350,f274]) ).
fof(f1107,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(not(X0),necessarily(not(X1))),necessarily(not(necessarily(possibly(and(not(X0),possibly(X1)))))))),
inference(forward_demodulation,[],[f1066,f287]) ).
fof(f1066,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(or(X0,necessarily(not(X1)))),necessarily(not(necessarily(possibly(and(not(X0),possibly(X1)))))))),
inference(superposition,[],[f339,f274]) ).
fof(f1065,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(or(X0,necessarily(not(X1))))),or(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f333,f274]) ).
fof(f1106,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,possibly(and(not(X0),possibly(X1)))),implies(strict_implies(not(X0),necessarily(not(X1))),X2))),
inference(forward_demodulation,[],[f1064,f287]) ).
fof(f1064,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,possibly(and(not(X0),possibly(X1)))),implies(necessarily(or(X0,necessarily(not(X1)))),X2))),
inference(superposition,[],[f330,f274]) ).
fof(f1063,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,or(X0,necessarily(not(X1)))))
| is_a_theorem(implies(and(not(X0),possibly(X1)),X2)) ),
inference(superposition,[],[f329,f274]) ).
fof(f1105,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(not(X0),necessarily(not(X1))),necessarily(possibly(possibly(and(not(X0),possibly(X1))))))),
inference(forward_demodulation,[],[f1061,f287]) ).
fof(f1061,plain,
! [X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),necessarily(possibly(possibly(and(not(X0),possibly(X1))))))),
inference(superposition,[],[f311,f274]) ).
fof(f1104,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),necessarily(not(X1))),or(possibly(and(not(X0),possibly(X1))),X2))),
inference(forward_demodulation,[],[f1060,f287]) ).
fof(f1060,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),or(possibly(and(not(X0),possibly(X1))),X2))),
inference(superposition,[],[f308,f274]) ).
fof(f1103,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),necessarily(not(X1))),or(X2,possibly(and(not(X0),possibly(X1)))))),
inference(forward_demodulation,[],[f1059,f287]) ).
fof(f1059,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),or(X2,possibly(and(not(X0),possibly(X1)))))),
inference(superposition,[],[f305,f274]) ).
fof(f1102,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),necessarily(not(X1))),implies(X2,possibly(and(not(X0),possibly(X1)))))),
inference(forward_demodulation,[],[f1058,f287]) ).
fof(f1058,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),implies(X2,possibly(and(not(X0),possibly(X1)))))),
inference(superposition,[],[f301,f274]) ).
fof(f1057,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),necessarily(possibly(or(X0,necessarily(not(X1))))))),
inference(superposition,[],[f300,f274]) ).
fof(f1056,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(or(X0,necessarily(not(X1))),X2))),
inference(superposition,[],[f299,f274]) ).
fof(f1055,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(X2,or(X0,necessarily(not(X1)))))),
inference(superposition,[],[f298,f274]) ).
fof(f1054,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(not(X0),possibly(X1)),and(X2,or(X0,necessarily(not(X1))))))),
inference(superposition,[],[f297,f274]) ).
fof(f1053,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(not(X0),possibly(X1)),and(X2,or(X0,necessarily(not(X1))))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f296,f274]) ).
fof(f1052,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),implies(X2,and(or(X0,necessarily(not(X1))),X2)))),
inference(superposition,[],[f295,f274]) ).
fof(f1051,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),implies(X2,or(X0,necessarily(not(X1)))))),
inference(superposition,[],[f294,f274]) ).
fof(f1050,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,necessarily(not(X1))),X2),or(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f292,f274]) ).
fof(f1049,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(or(X0,necessarily(not(X1))),X2),or(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f290,f274]) ).
fof(f1048,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,or(X0,necessarily(not(X1)))),or(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f289,f274]) ).
fof(f1101,plain,
! [X2,X0,X1] : implies(possibly(and(not(X0),possibly(X1))),X2) = or(strict_implies(not(X0),necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f1047,f287]) ).
fof(f1047,plain,
! [X2,X0,X1] : implies(possibly(and(not(X0),possibly(X1))),X2) = or(necessarily(or(X0,necessarily(not(X1)))),X2),
inference(superposition,[],[f281,f274]) ).
fof(f1046,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = implies(or(X0,necessarily(not(X1))),X2),
inference(superposition,[],[f277,f274]) ).
fof(f1045,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(not(X0),possibly(X1)))) = possibly(and(X2,or(X0,necessarily(not(X1))))),
inference(superposition,[],[f266,f274]) ).
fof(f1100,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),possibly(X1))))) = possibly(strict_implies(not(X0),necessarily(not(X1)))),
inference(forward_demodulation,[],[f1044,f287]) ).
fof(f1044,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),possibly(X1))))) = possibly(necessarily(or(X0,necessarily(not(X1))))),
inference(superposition,[],[f245,f274]) ).
fof(f1099,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = implies(or(X0,necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f1043,f219]) ).
fof(f1043,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = not(and(or(X0,necessarily(not(X1))),not(X2))),
inference(superposition,[],[f222,f274]) ).
fof(f1042,plain,
! [X2,X0,X1] : or(X2,and(not(X0),possibly(X1))) = not(and(not(X2),or(X0,necessarily(not(X1))))),
inference(superposition,[],[f222,f274]) ).
fof(f1098,plain,
! [X0,X1] : possibly(and(not(X0),possibly(X1))) = not(strict_implies(not(X0),necessarily(not(X1)))),
inference(forward_demodulation,[],[f1041,f287]) ).
fof(f1041,plain,
! [X0,X1] : possibly(and(not(X0),possibly(X1))) = not(necessarily(or(X0,necessarily(not(X1))))),
inference(superposition,[],[f221,f274]) ).
fof(f1040,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),possibly(X1))) = not(and(X2,or(X0,necessarily(not(X1))))),
inference(superposition,[],[f219,f274]) ).
fof(f1092,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),necessarily(not(X2))) = implies(or(X0,necessarily(not(X1))),necessarily(not(X2))),
inference(forward_demodulation,[],[f1034,f263]) ).
fof(f1034,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),necessarily(not(X2))) = not(and(or(X0,necessarily(not(X1))),possibly(X2))),
inference(superposition,[],[f274,f274]) ).
fof(f1033,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),necessarily(not(X2))) = not(and(implies(X0,necessarily(not(X1))),possibly(X2))),
inference(superposition,[],[f274,f263]) ).
fof(f1091,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),necessarily(not(X2))) = implies(or(X0,X1),necessarily(not(X2))),
inference(forward_demodulation,[],[f1032,f263]) ).
fof(f1032,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),necessarily(not(X2))) = not(and(or(X0,X1),possibly(X2))),
inference(superposition,[],[f274,f222]) ).
fof(f1090,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),necessarily(not(X2))) = implies(implies(X0,X1),necessarily(not(X2))),
inference(forward_demodulation,[],[f1031,f263]) ).
fof(f1031,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),necessarily(not(X2))) = not(and(implies(X0,X1),possibly(X2))),
inference(superposition,[],[f274,f219]) ).
fof(f1029,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(possibly(X0),necessarily(not(X0))),X1))
| ~ is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f942,f281]) ).
fof(f1028,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(or(X0,X0),X1)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(resolution,[],[f942,f358]) ).
fof(f1024,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(not(X1))))
| is_a_theorem(or(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f881,f281]) ).
fof(f1023,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,not(implies(X0,necessarily(not(X1))))))
| is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f881,f263]) ).
fof(f1022,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,not(or(X0,X1))))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f881,f222]) ).
fof(f1021,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,not(implies(X0,X1))))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f881,f219]) ).
fof(f613,plain,
! [X0,X1] :
( is_a_theorem(not(strict_implies(X0,X1)))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f262,f266]) ).
fof(f964,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(or(X1,possibly(X0))) ),
inference(resolution,[],[f330,f242]) ).
fof(f956,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(X0,possibly(X1)),and(not(X2),implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f437,f263]) ).
fof(f955,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(not(X0),not(X1)),and(not(X2),or(X0,X1))))),
inference(superposition,[],[f437,f222]) ).
fof(f954,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(X0,not(X1)),and(not(X2),implies(X0,X1))))),
inference(superposition,[],[f437,f219]) ).
fof(f952,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(X2,and(implies(X0,necessarily(not(X1))),not(X2))))),
inference(superposition,[],[f437,f263]) ).
fof(f951,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X2,and(or(X0,X1),not(X2))))),
inference(superposition,[],[f437,f222]) ).
fof(f950,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(X2,and(implies(X0,X1),not(X2))))),
inference(superposition,[],[f437,f219]) ).
fof(f946,plain,
! [X0,X1] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(not(X1)))
| ~ is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f818,f404]) ).
fof(f944,plain,
! [X0,X1] : is_a_theorem(implies(implies(necessarily(not(X0)),X1),implies(implies(possibly(X0),necessarily(not(X0))),X1))),
inference(superposition,[],[f784,f281]) ).
fof(f943,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),implies(or(not(X0),not(X0)),X1))),
inference(superposition,[],[f784,f277]) ).
fof(f925,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,or(X0,X1))) ),
inference(resolution,[],[f361,f242]) ).
fof(f918,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,necessarily(not(X1))),necessarily(not(necessarily(possibly(and(X0,possibly(X1)))))))),
inference(forward_demodulation,[],[f906,f218]) ).
fof(f906,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,necessarily(not(X1)))),necessarily(not(necessarily(possibly(and(X0,possibly(X1)))))))),
inference(superposition,[],[f339,f263]) ).
fof(f338,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f249,f245]) ).
fof(f886,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),not(not(X1))),or(X1,necessarily(not(X0))))),
inference(superposition,[],[f333,f281]) ).
fof(f885,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(implies(X0,necessarily(not(X1))))),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f333,f263]) ).
fof(f884,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(or(X0,X1))),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f333,f222]) ).
fof(f883,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(implies(X0,X1))),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f333,f219]) ).
fof(f864,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),and(implies(X0,necessarily(not(X1))),implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f755,f263]) ).
fof(f863,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,implies(X0,necessarily(not(X1)))),implies(X2,and(X0,possibly(X1))))),
inference(superposition,[],[f746,f263]) ).
fof(f862,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f742,f263]) ).
fof(f878,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X0,necessarily(not(X1))),implies(possibly(and(X0,possibly(X1))),X2))),
inference(forward_demodulation,[],[f861,f218]) ).
fof(f861,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(implies(X0,necessarily(not(X1)))),implies(possibly(and(X0,possibly(X1))),X2))),
inference(superposition,[],[f653,f263]) ).
fof(f858,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(implies(X0,necessarily(not(X1))),X2))
| is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f410,f263]) ).
fof(f857,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X2,implies(X0,necessarily(not(X1)))))
| is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f406,f263]) ).
fof(f856,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,necessarily(not(X1))),X2))
| ~ is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f404,f263]) ).
fof(f855,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,necessarily(not(X1))),X2))
| is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f402,f263]) ).
fof(f851,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,necessarily(not(X1)))))
| is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f350,f263]) ).
fof(f850,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,necessarily(not(X1)))))
| is_a_theorem(implies(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f329,f263]) ).
fof(f875,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),necessarily(possibly(possibly(and(X0,possibly(X1))))))),
inference(forward_demodulation,[],[f848,f218]) ).
fof(f848,plain,
! [X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),necessarily(possibly(possibly(and(X0,possibly(X1))))))),
inference(superposition,[],[f311,f263]) ).
fof(f874,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),or(possibly(and(X0,possibly(X1))),X2))),
inference(forward_demodulation,[],[f847,f218]) ).
fof(f847,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),or(possibly(and(X0,possibly(X1))),X2))),
inference(superposition,[],[f308,f263]) ).
fof(f873,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),or(X2,possibly(and(X0,possibly(X1)))))),
inference(forward_demodulation,[],[f846,f218]) ).
fof(f846,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),or(X2,possibly(and(X0,possibly(X1)))))),
inference(superposition,[],[f305,f263]) ).
fof(f872,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),implies(X2,possibly(and(X0,possibly(X1)))))),
inference(forward_demodulation,[],[f845,f218]) ).
fof(f845,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),implies(X2,possibly(and(X0,possibly(X1)))))),
inference(superposition,[],[f301,f263]) ).
fof(f844,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),necessarily(possibly(implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f300,f263]) ).
fof(f843,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(implies(X0,necessarily(not(X1))),X2))),
inference(superposition,[],[f299,f263]) ).
fof(f842,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(X2,implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f298,f263]) ).
fof(f841,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(X0,possibly(X1)),and(X2,implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f297,f263]) ).
fof(f840,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,possibly(X1)),and(X2,implies(X0,necessarily(not(X1))))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f296,f263]) ).
fof(f839,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X2,and(implies(X0,necessarily(not(X1))),X2)))),
inference(superposition,[],[f295,f263]) ).
fof(f838,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X2,implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f294,f263]) ).
fof(f837,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,necessarily(not(X1))),X2),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f292,f263]) ).
fof(f836,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(implies(X0,necessarily(not(X1))),X2),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f290,f263]) ).
fof(f835,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,implies(X0,necessarily(not(X1)))),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f289,f263]) ).
fof(f871,plain,
! [X2,X0,X1] : implies(possibly(and(X0,possibly(X1))),X2) = or(strict_implies(X0,necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f834,f218]) ).
fof(f834,plain,
! [X2,X0,X1] : implies(possibly(and(X0,possibly(X1))),X2) = or(necessarily(implies(X0,necessarily(not(X1)))),X2),
inference(superposition,[],[f281,f263]) ).
fof(f833,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),X2) = implies(implies(X0,necessarily(not(X1))),X2),
inference(superposition,[],[f277,f263]) ).
fof(f832,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(X0,possibly(X1)))) = possibly(and(X2,implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f266,f263]) ).
fof(f870,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,possibly(X1))))) = possibly(strict_implies(X0,necessarily(not(X1)))),
inference(forward_demodulation,[],[f831,f218]) ).
fof(f831,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,possibly(X1))))) = possibly(necessarily(implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f245,f263]) ).
fof(f830,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),X2) = not(and(implies(X0,necessarily(not(X1))),not(X2))),
inference(superposition,[],[f222,f263]) ).
fof(f829,plain,
! [X2,X0,X1] : or(X2,and(X0,possibly(X1))) = not(and(not(X2),implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f222,f263]) ).
fof(f869,plain,
! [X0,X1] : not(strict_implies(X0,necessarily(not(X1)))) = possibly(and(X0,possibly(X1))),
inference(forward_demodulation,[],[f828,f218]) ).
fof(f828,plain,
! [X0,X1] : possibly(and(X0,possibly(X1))) = not(necessarily(implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f221,f263]) ).
fof(f827,plain,
! [X2,X0,X1] : implies(X2,and(X0,possibly(X1))) = not(and(X2,implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f219,f263]) ).
fof(f822,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(necessarily(X2),strict_implies(not(X0),X1)))
| ~ is_a_theorem(strict_implies(X2,or(X0,X1))) ),
inference(superposition,[],[f575,f287]) ).
fof(f821,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(necessarily(X2),strict_implies(X0,X1)))
| ~ is_a_theorem(strict_implies(X2,implies(X0,X1))) ),
inference(superposition,[],[f575,f218]) ).
fof(f820,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(strict_implies(not(X0),X1),necessarily(X2)))
| ~ is_a_theorem(strict_implies(or(X0,X1),X2)) ),
inference(superposition,[],[f575,f287]) ).
fof(f819,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(strict_implies(X0,X1),necessarily(X2)))
| ~ is_a_theorem(strict_implies(implies(X0,X1),X2)) ),
inference(superposition,[],[f575,f218]) ).
fof(f815,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X0,X1))),
inference(superposition,[],[f746,f277]) ).
fof(f814,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,or(X0,X1)),implies(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f746,f222]) ).
fof(f813,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,implies(X0,X1)),implies(X2,and(X0,not(X1))))),
inference(superposition,[],[f746,f219]) ).
fof(f812,plain,
! [X0,X1] : is_a_theorem(or(and(X1,possibly(X0)),implies(X1,necessarily(not(X0))))),
inference(superposition,[],[f746,f221]) ).
fof(f762,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(superposition,[],[f752,f220]) ).
fof(f795,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),and(or(X0,X1),or(X0,X1)))),
inference(superposition,[],[f755,f222]) ).
fof(f794,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),and(implies(X0,X1),implies(X0,X1)))),
inference(superposition,[],[f755,f219]) ).
fof(f791,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(resolution,[],[f753,f242]) ).
fof(f786,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),X1)))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(resolution,[],[f244,f242]) ).
fof(f754,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f728,f223]) ).
fof(f747,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X0,X1))),
inference(superposition,[],[f742,f222]) ).
fof(f739,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,or(X0,X1))) ),
inference(forward_demodulation,[],[f738,f277]) ).
fof(f738,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f735,f277]) ).
fof(f735,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,implies(not(X0),X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f358,f277]) ).
fof(f732,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),implies(X0,X0))),
inference(resolution,[],[f358,f243]) ).
fof(f726,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X2),implies(implies(X2,X1),or(X0,X1)))),
inference(forward_demodulation,[],[f724,f277]) ).
fof(f724,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X0),X2),implies(implies(X2,X1),or(X0,X1)))),
inference(superposition,[],[f243,f277]) ).
fof(f655,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f251,f281]) ).
fof(f692,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f653,f242]) ).
fof(f612,plain,
! [X0,X1] :
( is_a_theorem(necessarily(not(strict_implies(X0,X1))))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f249,f266]) ).
fof(f610,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(not(X0),not(X1)))) = possibly(and(X2,or(X0,X1))),
inference(superposition,[],[f266,f222]) ).
fof(f609,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(X0,not(X1)))) = possibly(and(X2,implies(X0,X1))),
inference(superposition,[],[f266,f219]) ).
fof(f608,plain,
! [X0,X1] : not(strict_implies(X1,necessarily(not(X0)))) = possibly(and(X1,possibly(X0))),
inference(superposition,[],[f266,f221]) ).
fof(f579,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,or(X0,X1)),implies(necessarily(X2),strict_implies(not(X0),X1)))),
inference(superposition,[],[f529,f287]) ).
fof(f577,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),implies(strict_implies(not(X0),X1),necessarily(X2)))),
inference(superposition,[],[f529,f287]) ).
fof(f528,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(or(X0,X1),X2))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f410,f222]) ).
fof(f527,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(implies(X0,X1),X2))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f410,f219]) ).
fof(f526,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(possibly(X0),X1))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f410,f221]) ).
fof(f410,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f290,f242]) ).
fof(f525,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X2,or(X0,X1)))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f406,f222]) ).
fof(f524,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X2,implies(X0,X1)))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f406,f219]) ).
fof(f523,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X1,possibly(X0)))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f406,f221]) ).
fof(f406,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X1,not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f289,f242]) ).
fof(f521,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(or(X0,X1),X2))
| ~ is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f404,f222]) ).
fof(f520,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,X1),X2))
| ~ is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f404,f219]) ).
fof(f519,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f404,f221]) ).
fof(f515,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(or(X0,X1),X2))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f402,f222]) ).
fof(f514,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f402,f219]) ).
fof(f513,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(X0),X1))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f402,f221]) ).
fof(f337,plain,
! [X0] :
( is_a_theorem(not(necessarily(possibly(X0))))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f262,f245]) ).
fof(f495,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),necessarily(possibly(possibly(and(not(X0),not(X1))))))),
inference(forward_demodulation,[],[f490,f287]) ).
fof(f490,plain,
! [X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),necessarily(possibly(possibly(and(not(X0),not(X1))))))),
inference(superposition,[],[f311,f222]) ).
fof(f494,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(X0,X1),necessarily(possibly(possibly(and(X0,not(X1))))))),
inference(forward_demodulation,[],[f489,f218]) ).
fof(f489,plain,
! [X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),necessarily(possibly(possibly(and(X0,not(X1))))))),
inference(superposition,[],[f311,f219]) ).
fof(f485,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),or(possibly(and(not(X0),not(X1))),X2))),
inference(forward_demodulation,[],[f480,f287]) ).
fof(f480,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),or(possibly(and(not(X0),not(X1))),X2))),
inference(superposition,[],[f308,f222]) ).
fof(f484,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),or(possibly(and(X0,not(X1))),X2))),
inference(forward_demodulation,[],[f479,f218]) ).
fof(f479,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),or(possibly(and(X0,not(X1))),X2))),
inference(superposition,[],[f308,f219]) ).
fof(f476,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f270,f223]) ).
fof(f473,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f253,f223]) ).
fof(f472,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(superposition,[],[f234,f223]) ).
fof(f466,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),or(X2,possibly(and(not(X0),not(X1)))))),
inference(forward_demodulation,[],[f461,f287]) ).
fof(f461,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),or(X2,possibly(and(not(X0),not(X1)))))),
inference(superposition,[],[f305,f222]) ).
fof(f465,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),or(X2,possibly(and(X0,not(X1)))))),
inference(forward_demodulation,[],[f460,f218]) ).
fof(f460,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),or(X2,possibly(and(X0,not(X1)))))),
inference(superposition,[],[f305,f219]) ).
fof(f452,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X1)),or(X0,possibly(X1)))),
inference(superposition,[],[f301,f277]) ).
fof(f456,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),implies(X2,possibly(and(not(X0),not(X1)))))),
inference(forward_demodulation,[],[f450,f287]) ).
fof(f450,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),implies(X2,possibly(and(not(X0),not(X1)))))),
inference(superposition,[],[f301,f222]) ).
fof(f455,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),implies(X2,possibly(and(X0,not(X1)))))),
inference(forward_demodulation,[],[f449,f218]) ).
fof(f449,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),implies(X2,possibly(and(X0,not(X1)))))),
inference(superposition,[],[f301,f219]) ).
fof(f446,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,and(not(X0),not(X1))))),
inference(superposition,[],[f297,f277]) ).
fof(f445,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(not(X0),not(X1)),and(X2,or(X0,X1))))),
inference(superposition,[],[f297,f222]) ).
fof(f444,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(X0,not(X1)),and(X2,implies(X0,X1))))),
inference(superposition,[],[f297,f219]) ).
fof(f443,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(necessarily(not(X0)),and(X1,possibly(X0))))),
inference(superposition,[],[f297,f221]) ).
fof(f441,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(not(X0),not(X1)),and(X2,or(X0,X1))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f296,f222]) ).
fof(f440,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,not(X1)),and(X2,implies(X0,X1))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f296,f219]) ).
fof(f439,plain,
! [X0,X1] :
( is_a_theorem(or(necessarily(not(X0)),and(X1,possibly(X0))))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f296,f221]) ).
fof(f296,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f253,f277]) ).
fof(f436,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),implies(X2,and(or(X0,X1),X2)))),
inference(superposition,[],[f295,f222]) ).
fof(f435,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X2,and(implies(X0,X1),X2)))),
inference(superposition,[],[f295,f219]) ).
fof(f434,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),implies(X1,and(possibly(X0),X1)))),
inference(superposition,[],[f295,f221]) ).
fof(f429,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f257,f220]) ).
fof(f428,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f256,f220]) ).
fof(f432,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_equiv(X1,X0)) ),
inference(resolution,[],[f425,f242]) ).
fof(f431,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[],[f424,f242]) ).
fof(f430,plain,
! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f270,f220]) ).
fof(f427,plain,
! [X0,X1] :
( is_a_theorem(implies(strict_implies(X1,X0),strict_equiv(X0,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f253,f220]) ).
fof(f423,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f292,f222]) ).
fof(f422,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,X1),X2),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f292,f219]) ).
fof(f421,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(possibly(X0),X1),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f292,f221]) ).
fof(f420,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(strict_implies(not(X0),X1)) ),
inference(resolution,[],[f292,f242]) ).
fof(f291,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f242,f277]) ).
fof(f413,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(or(X0,X1),X2),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f290,f222]) ).
fof(f412,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(implies(X0,X1),X2),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f290,f219]) ).
fof(f411,plain,
! [X0,X1] : is_a_theorem(implies(equiv(possibly(X0),X1),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f290,f221]) ).
fof(f409,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,or(X0,X1)),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f289,f222]) ).
fof(f408,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,implies(X0,X1)),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f289,f219]) ).
fof(f407,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X1,possibly(X0)),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f289,f221]) ).
fof(f405,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f225,f287]) ).
fof(f398,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(or(X0,X1)))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f350,f222]) ).
fof(f397,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,X1)))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f350,f219]) ).
fof(f396,plain,
! [X0,X1] :
( ~ is_a_theorem(not(possibly(X0)))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f350,f221]) ).
fof(f362,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[],[f360,f277]) ).
fof(f360,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),or(X0,X1)),or(X0,X1))),
inference(superposition,[],[f238,f277]) ).
fof(f348,plain,
! [X0,X1] :
( ~ is_a_theorem(not(X0))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f344,f242]) ).
fof(f349,plain,
~ is_a_theorem(not(and(sK0,sK1))),
inference(resolution,[],[f344,f268]) ).
fof(f347,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(not(X0),not(X1)),X2))
| ~ is_a_theorem(or(X2,or(X0,X1))) ),
inference(superposition,[],[f329,f222]) ).
fof(f346,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[],[f329,f219]) ).
fof(f345,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(or(X1,possibly(X0))) ),
inference(superposition,[],[f329,f221]) ).
fof(f336,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),not(X1))))) = possibly(necessarily(or(X0,X1))),
inference(superposition,[],[f245,f222]) ).
fof(f341,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,not(X1))))) = possibly(strict_implies(X0,X1)),
inference(forward_demodulation,[],[f335,f218]) ).
fof(f335,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,not(X1))))) = possibly(necessarily(implies(X0,X1))),
inference(superposition,[],[f245,f219]) ).
fof(f319,plain,
( ~ is_a_theorem(sK1)
| ~ is_a_theorem(sK0) ),
inference(resolution,[],[f270,f315]) ).
fof(f315,plain,
~ is_a_theorem(and(sK1,sK0)),
inference(resolution,[],[f268,f252]) ).
fof(f313,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),necessarily(possibly(or(X0,X1))))),
inference(superposition,[],[f300,f222]) ).
fof(f312,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),necessarily(possibly(implies(X0,X1))))),
inference(superposition,[],[f300,f219]) ).
fof(f310,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(or(X0,X1),X2))),
inference(superposition,[],[f299,f222]) ).
fof(f309,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(implies(X0,X1),X2))),
inference(superposition,[],[f299,f219]) ).
fof(f307,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X2,or(X0,X1)))),
inference(superposition,[],[f298,f222]) ).
fof(f306,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(X2,implies(X0,X1)))),
inference(superposition,[],[f298,f219]) ).
fof(f304,plain,
! [X0,X1] : is_a_theorem(or(X1,or(X0,not(X1)))),
inference(superposition,[],[f294,f277]) ).
fof(f303,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),implies(X2,or(X0,X1)))),
inference(superposition,[],[f294,f222]) ).
fof(f302,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X2,implies(X0,X1)))),
inference(superposition,[],[f294,f219]) ).
fof(f286,plain,
! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(superposition,[],[f277,f222]) ).
fof(f285,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f277,f219]) ).
fof(f284,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(superposition,[],[f277,f221]) ).
fof(f280,plain,
! [X0,X1] : possibly(and(not(X0),not(X1))) = not(necessarily(or(X0,X1))),
inference(superposition,[],[f221,f222]) ).
fof(f278,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f219,f222]) ).
fof(f255,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f242,f236]) ).
fof(f254,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X1,X0))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f242,f235]) ).
fof(f269,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f248,f242]) ).
fof(f257,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X1,X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f242,f233]) ).
fof(f256,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) ),
inference(resolution,[],[f242,f232]) ).
fof(f251,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f242,f230]) ).
fof(f262,plain,
! [X0] :
( is_a_theorem(possibly(X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f249,f258]) ).
fof(f249,plain,
! [X0] :
( is_a_theorem(necessarily(possibly(X0)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f242,f226]) ).
fof(f98508,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98365]) ).
fof(f98365,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11863]) ).
fof(f11863,plain,
! [X0] : is_a_theorem(possibly(implies(X0,X0))),
inference(resolution,[],[f10251,f235]) ).
fof(f10251,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f9819,f6790]) ).
fof(f6790,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(possibly(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f6085,f242]) ).
fof(f6085,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,possibly(X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f6057,f1715]) ).
fof(f98507,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98377]) ).
fof(f98377,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11871]) ).
fof(f11871,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,equiv(X1,X1)))),
inference(resolution,[],[f10251,f231]) ).
fof(f98506,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98379]) ).
fof(f98379,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11872]) ).
fof(f11872,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,and(equiv(X1,X1),X0)))),
inference(resolution,[],[f10251,f234]) ).
fof(f98505,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98380]) ).
fof(f98380,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12205]) ).
fof(f12205,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,and(strict_equiv(X1,X1),X0)))),
inference(resolution,[],[f10274,f234]) ).
fof(f10274,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(strict_equiv(X1,X1),X0))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f9831,f6790]) ).
fof(f98504,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98381]) ).
fof(f98381,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12204]) ).
fof(f12204,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,strict_equiv(X1,X1)))),
inference(resolution,[],[f10274,f231]) ).
fof(f98503,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98383]) ).
fof(f98383,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24857]) ).
fof(f24857,plain,
( ! [X0,X1] : is_a_theorem(possibly(implies(necessarily(not(equiv(X0,X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f20962,f10251]) ).
fof(f98502,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98384]) ).
fof(f98384,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f24861]) ).
fof(f24861,plain,
( ! [X0,X1] : is_a_theorem(possibly(implies(necessarily(not(strict_equiv(X0,X0))),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f20962,f10274]) ).
fof(f98501,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98386]) ).
fof(f98386,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f7095]) ).
fof(f7095,plain,
! [X0] : is_a_theorem(possibly(equiv(X0,X0))),
inference(subsumption_resolution,[],[f7033,f727]) ).
fof(f7033,plain,
! [X0] :
( is_a_theorem(possibly(equiv(X0,X0)))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f6790,f731]) ).
fof(f98500,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98390]) ).
fof(f98390,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18122]) ).
fof(f18122,plain,
( ! [X0] : is_a_theorem(possibly(not(not(equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f10251]) ).
fof(f98499,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98391]) ).
fof(f98391,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f18126]) ).
fof(f18126,plain,
( ! [X0] : is_a_theorem(possibly(not(not(strict_equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f18103,f10274]) ).
fof(f98498,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98393]) ).
fof(f98393,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23170]) ).
fof(f23170,plain,
( ! [X0,X1] : is_a_theorem(possibly(not(and(not(equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f19264,f10251]) ).
fof(f98497,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98394]) ).
fof(f98394,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23174]) ).
fof(f23174,plain,
( ! [X0,X1] : is_a_theorem(possibly(not(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f19264,f10274]) ).
fof(f98496,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98396]) ).
fof(f98396,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23657]) ).
fof(f23657,plain,
( ! [X0] : is_a_theorem(possibly(not(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f20197,f10251]) ).
fof(f98495,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98397]) ).
fof(f98397,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f23661]) ).
fof(f23661,plain,
( ! [X0] : is_a_theorem(possibly(not(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl2_7 ),
inference(resolution,[],[f20197,f10274]) ).
fof(f98494,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98406]) ).
fof(f98406,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11877]) ).
fof(f11877,plain,
! [X0] : is_a_theorem(possibly(and(equiv(X0,X0),equiv(X0,X0)))),
inference(resolution,[],[f10251,f728]) ).
fof(f98493,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98407]) ).
fof(f98407,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11880]) ).
fof(f11880,plain,
! [X0,X1] : is_a_theorem(possibly(and(equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10251,f10400]) ).
fof(f98492,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98409]) ).
fof(f98409,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12213]) ).
fof(f12213,plain,
! [X0,X1] : is_a_theorem(possibly(and(equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10274,f10400]) ).
fof(f98491,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98410]) ).
fof(f98410,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12210]) ).
fof(f12210,plain,
! [X0] : is_a_theorem(possibly(and(strict_equiv(X0,X0),strict_equiv(X0,X0)))),
inference(resolution,[],[f10274,f728]) ).
fof(f98490,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98411]) ).
fof(f98411,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12214]) ).
fof(f12214,plain,
! [X0,X1] : is_a_theorem(possibly(and(strict_equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10274,f10704]) ).
fof(f98489,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98413]) ).
fof(f98413,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11881]) ).
fof(f11881,plain,
! [X0,X1] : is_a_theorem(possibly(and(strict_equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10251,f10704]) ).
fof(f98488,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98421]) ).
fof(f98421,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11886]) ).
fof(f11886,plain,
! [X0,X1] : is_a_theorem(possibly(or(X0,equiv(X1,X1)))),
inference(resolution,[],[f10251,f229]) ).
fof(f98487,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98422]) ).
fof(f98422,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11865]) ).
fof(f11865,plain,
! [X0] : is_a_theorem(possibly(or(X0,not(X0)))),
inference(resolution,[],[f10251,f289]) ).
fof(f98486,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98424]) ).
fof(f98424,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12219]) ).
fof(f12219,plain,
! [X0,X1] : is_a_theorem(possibly(or(X0,strict_equiv(X1,X1)))),
inference(resolution,[],[f10274,f229]) ).
fof(f98485,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98425]) ).
fof(f98425,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11892]) ).
fof(f11892,plain,
! [X0,X1] : is_a_theorem(possibly(or(equiv(X0,X0),X1))),
inference(resolution,[],[f10251,f230]) ).
fof(f98484,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98426]) ).
fof(f98426,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12225]) ).
fof(f12225,plain,
! [X0,X1] : is_a_theorem(possibly(or(strict_equiv(X0,X0),X1))),
inference(resolution,[],[f10274,f230]) ).
fof(f98483,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98430]) ).
fof(f98430,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11893]) ).
fof(f11893,plain,
! [X0] : is_a_theorem(possibly(necessarily(possibly(equiv(X0,X0))))),
inference(resolution,[],[f10251,f226]) ).
fof(f98482,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98431]) ).
fof(f98431,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12226]) ).
fof(f12226,plain,
! [X0] : is_a_theorem(possibly(necessarily(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f10274,f226]) ).
fof(f98481,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98438]) ).
fof(f98438,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12198]) ).
fof(f12198,plain,
! [X0] : is_a_theorem(possibly(strict_implies(X0,X0))),
inference(resolution,[],[f10274,f424]) ).
fof(f98480,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98440]) ).
fof(f98440,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45626]) ).
fof(f45626,plain,
( ! [X0,X1] : is_a_theorem(possibly(strict_implies(not(equiv(X0,X0)),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f41539,f18452]) ).
fof(f18452,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(possibly(X0)) )
| ~ spl2_7 ),
inference(resolution,[],[f18413,f2963]) ).
fof(f98479,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98441]) ).
fof(f98441,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f45656]) ).
fof(f45656,plain,
( ! [X0,X1] : is_a_theorem(possibly(strict_implies(not(strict_equiv(X0,X0)),X1)))
| ~ spl2_7 ),
inference(resolution,[],[f41567,f18452]) ).
fof(f98478,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98442]) ).
fof(f98442,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f7099]) ).
fof(f7099,plain,
! [X0] : is_a_theorem(possibly(strict_equiv(X0,X0))),
inference(subsumption_resolution,[],[f7079,f1913]) ).
fof(f7079,plain,
! [X0] :
( is_a_theorem(possibly(strict_equiv(X0,X0)))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(resolution,[],[f6790,f753]) ).
fof(f98477,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98447]) ).
fof(f98447,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f92696]) ).
fof(f92696,plain,
( ! [X0] : is_a_theorem(possibly(possibly(implies(X0,X0))))
| ~ spl2_7 ),
inference(resolution,[],[f92662,f20783]) ).
fof(f20783,plain,
( ! [X0] :
( ~ is_a_theorem(or(possibly(X0),X0))
| is_a_theorem(possibly(possibly(X0))) )
| ~ spl2_7 ),
inference(resolution,[],[f18428,f6801]) ).
fof(f6801,plain,
! [X0,X1] :
( is_a_theorem(or(X0,possibly(X1)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f6800,f277]) ).
fof(f6800,plain,
! [X0,X1] :
( is_a_theorem(or(X0,possibly(X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f6085,f277]) ).
fof(f18428,plain,
( ! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(possibly(X0)) )
| ~ spl2_7 ),
inference(resolution,[],[f18418,f2180]) ).
fof(f98476,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98448]) ).
fof(f98448,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f11729]) ).
fof(f11729,plain,
! [X0] : is_a_theorem(possibly(possibly(equiv(X0,X0)))),
inference(resolution,[],[f11701,f7074]) ).
fof(f7074,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f6790,f6074]) ).
fof(f98475,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98450]) ).
fof(f98450,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f33805]) ).
fof(f33805,plain,
( ! [X0] : is_a_theorem(possibly(possibly(not(not(equiv(X0,X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f20783,f27601]) ).
fof(f98474,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98451]) ).
fof(f98451,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f33806]) ).
fof(f33806,plain,
( ! [X0] : is_a_theorem(possibly(possibly(not(not(strict_equiv(X0,X0))))))
| ~ spl2_7 ),
inference(resolution,[],[f20783,f28269]) ).
fof(f98473,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98456]) ).
fof(f98456,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f95316]) ).
fof(f95316,plain,
( ! [X0] : is_a_theorem(possibly(possibly(or(X0,not(X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f93823,f20783]) ).
fof(f98472,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98461]) ).
fof(f98461,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f47193]) ).
fof(f47193,plain,
( ! [X0,X1] : is_a_theorem(possibly(possibly(strict_implies(not(equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f45627,f20783]) ).
fof(f98471,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98462]) ).
fof(f98462,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f47835]) ).
fof(f47835,plain,
( ! [X0,X1] : is_a_theorem(possibly(possibly(strict_implies(not(strict_equiv(X0,X0)),X1))))
| ~ spl2_7 ),
inference(resolution,[],[f45657,f20783]) ).
fof(f98470,plain,
~ spl2_8,
inference(avatar_contradiction_clause,[],[f98463]) ).
fof(f98463,plain,
( $false
| ~ spl2_8 ),
inference(resolution,[],[f18106,f12111]) ).
fof(f12111,plain,
! [X0] : is_a_theorem(possibly(possibly(strict_equiv(X0,X0)))),
inference(resolution,[],[f12086,f7074]) ).
fof(f98469,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98466]) ).
fof(f98466,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f33821]) ).
fof(f33821,plain,
( ! [X0] : is_a_theorem(possibly(possibly(possibly(equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f20783,f11730]) ).
fof(f98468,plain,
( ~ spl2_7
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f98467]) ).
fof(f98467,plain,
( $false
| ~ spl2_7
| ~ spl2_8 ),
inference(resolution,[],[f18106,f33822]) ).
fof(f33822,plain,
( ! [X0] : is_a_theorem(possibly(possibly(possibly(strict_equiv(X0,X0)))))
| ~ spl2_7 ),
inference(resolution,[],[f20783,f12112]) ).
fof(f97510,plain,
( spl2_8
| spl2_9 ),
inference(avatar_split_clause,[],[f92632,f97508,f18105]) ).
fof(f97508,plain,
( spl2_9
<=> ! [X0] : is_a_theorem(necessarily(possibly(implies(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f92632,plain,
! [X0,X1] :
( is_a_theorem(necessarily(possibly(implies(X0,X0))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f92525,f8204]) ).
fof(f8204,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(possibly(X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5932,f242]) ).
fof(f5932,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,necessarily(possibly(X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1715,f226]) ).
fof(f18107,plain,
( spl2_7
| spl2_8 ),
inference(avatar_split_clause,[],[f18050,f18105,f18102]) ).
fof(f18050,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,not(not(X1)))) ),
inference(resolution,[],[f11348,f5951]) ).
fof(f11348,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,and(X1,not(not(X0)))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1332,f5789]) ).
fof(f3657,plain,
( ~ spl2_5
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f3640,f3654,f3650]) ).
fof(f3650,plain,
( spl2_5
<=> is_a_theorem(necessarily(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f3654,plain,
( spl2_6
<=> is_a_theorem(necessarily(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f3640,plain,
( ~ is_a_theorem(necessarily(sK0))
| ~ is_a_theorem(necessarily(sK1)) ),
inference(resolution,[],[f1629,f315]) ).
fof(f383,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f364,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f353,f268]) ).
fof(f353,plain,
( ! [X1] : is_a_theorem(X1)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f352,plain,
( spl2_3
<=> ! [X1] : is_a_theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f382,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f368,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f353,f349]) ).
fof(f381,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f371,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f353,f315]) ).
fof(f380,plain,
~ spl2_3,
inference(avatar_contradiction_clause,[],[f374]) ).
fof(f374,plain,
( $false
| ~ spl2_3 ),
inference(resolution,[],[f353,f224]) ).
fof(f379,plain,
( spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f376]) ).
fof(f376,plain,
( $false
| spl2_1
| ~ spl2_3 ),
inference(resolution,[],[f353,f323]) ).
fof(f323,plain,
( ~ is_a_theorem(sK0)
| spl2_1 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f321,plain,
( spl2_1
<=> is_a_theorem(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f378,plain,
( spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f377,plain,
( $false
| spl2_2
| ~ spl2_3 ),
inference(resolution,[],[f353,f327]) ).
fof(f327,plain,
( ~ is_a_theorem(sK1)
| spl2_2 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f325,plain,
( spl2_2
<=> is_a_theorem(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f357,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f348,f355,f352]) ).
fof(f355,plain,
( spl2_4
<=> ! [X0] :
( ~ is_a_theorem(not(X0))
| ~ is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f328,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f319,f325,f321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL541+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.11/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri May 3 13:12:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (19403)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.35 % (19406)WARNING: value z3 for option sas not known
% 0.18/0.35 % (19405)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.35 % (19410)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)
% 0.18/0.35 % (19404)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.35 % (19409)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)
% 0.18/0.35 % (19407)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.35 % (19406)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)
% 0.18/0.35 % (19408)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)
% 0.18/0.35 TRYING [1]
% 0.18/0.35 TRYING [2]
% 0.18/0.36 TRYING [1]
% 0.18/0.36 TRYING [3]
% 0.18/0.36 TRYING [2]
% 0.18/0.37 TRYING [3]
% 0.18/0.37 TRYING [4]
% 0.18/0.43 TRYING [4]
% 0.18/0.46 TRYING [5]
% 2.21/0.64 TRYING [5]
% 2.94/0.76 TRYING [6]
% 7.42/1.45 TRYING [1]
% 7.42/1.45 TRYING [2]
% 7.42/1.45 TRYING [3]
% 7.97/1.47 TRYING [7]
% 7.97/1.47 TRYING [4]
% 8.38/1.53 TRYING [5]
% 9.08/1.64 TRYING [6]
% 9.62/1.78 TRYING [6]
% 15.25/2.55 TRYING [7]
% 33.44/5.13 TRYING [8]
% 51.95/7.80 TRYING [8]
% 79.05/11.67 TRYING [9]
% 90.63/13.35 TRYING [9]
% 98.82/14.58 TRYING [7]
% 245.37/35.43 TRYING [10]
% 298.66/43.05 % (19406)First to succeed.
% 298.66/43.07 % (19406)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19403"
% 299.30/43.08 % (19406)Refutation found. Thanks to Tanya!
% 299.30/43.08 % SZS status Theorem for theBenchmark
% 299.30/43.08 % SZS output start Proof for theBenchmark
% See solution above
% 299.33/43.10 % (19406)------------------------------
% 299.33/43.10 % (19406)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 299.33/43.10 % (19406)Termination reason: Refutation
% 299.33/43.10
% 299.33/43.10 % (19406)Memory used [KB]: 128091
% 299.33/43.10 % (19406)Time elapsed: 42.730 s
% 299.33/43.10 % (19406)Instructions burned: 165360 (million)
% 299.33/43.10 % (19403)Success in time 42.509 s
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