TSTP Solution File: LCL549+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL549+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:44:49 EDT 2024
% Result : Theorem 108.75s 15.97s
% Output : Refutation 108.75s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f149781,plain,
$false,
inference(avatar_sat_refutation,[],[f350,f18097,f97475,f98433,f98434,f98435,f98436,f98437,f98438,f98439,f98440,f98441,f98442,f98443,f98444,f98445,f98446,f98447,f98448,f98449,f98450,f98451,f98452,f98453,f98454,f98455,f98456,f98457,f98458,f98459,f98460,f98461,f98462,f98463,f98464,f98465,f98466,f98467,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,f149760]) ).
fof(f149760,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f149719]) ).
fof(f149719,plain,
( $false
| ~ spl1_3 ),
inference(resolution,[],[f137254,f268]) ).
fof(f268,plain,
~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))),
inference(resolution,[],[f247,f224]) ).
fof(f224,plain,
~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(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_m10
| ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f137,f159]) ).
fof(f159,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
=> ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
( axiom_m10
| ? [X0] : ~ is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_m10 ),
inference(unused_predicate_definition_removal,[],[f72]) ).
fof(f72,axiom,
( axiom_m10
<=> ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m10) ).
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_m10,
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
~ axiom_m10,
inference(flattening,[],[f90]) ).
fof(f90,negated_conjecture,
~ axiom_m10,
inference(negated_conjecture,[],[f89]) ).
fof(f89,conjecture,
axiom_m10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m10_axiom_m10) ).
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(f137254,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f226,f136443]) ).
fof(f136443,plain,
( ! [X0] : possibly(X0) = possibly(possibly(X0))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f136442,f221]) ).
fof(f136442,plain,
( ! [X0] : possibly(possibly(X0)) = not(necessarily(not(X0)))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f136116,f119376]) ).
fof(f119376,plain,
! [X0] : necessarily(X0) = necessarily(necessarily(X0)),
inference(subsumption_resolution,[],[f119183,f225]) ).
fof(f119183,plain,
! [X0] :
( ~ is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0)))
| necessarily(X0) = necessarily(necessarily(X0)) ),
inference(resolution,[],[f5570,f227]) ).
fof(f5570,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| X0 = X1 ),
inference(resolution,[],[f1570,f241]) ).
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(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(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(f1570,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f575,f242]) ).
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(f575,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f240,f242]) ).
fof(f136116,plain,
( ! [X0] : possibly(possibly(X0)) = not(necessarily(necessarily(not(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f120920,f221]) ).
fof(f120920,plain,
( ! [X0] : possibly(not(X0)) = not(necessarily(X0))
| ~ spl1_3 ),
inference(superposition,[],[f221,f119305]) ).
fof(f119305,plain,
( ! [X0] : not(not(X0)) = X0
| ~ spl1_3 ),
inference(subsumption_resolution,[],[f119304,f18238]) ).
fof(f18238,plain,
( ! [X0] : is_a_theorem(or(not(X0),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18137,f855]) ).
fof(f855,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f326,f242]) ).
fof(f326,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(not(X0))),or(X0,X1))),
inference(superposition,[],[f318,f279]) ).
fof(f279,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f222,f219]) ).
fof(f318,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(forward_demodulation,[],[f237,f279]) ).
fof(f18137,plain,
( ! [X0] : is_a_theorem(or(X0,not(not(not(X0)))))
| ~ spl1_3 ),
inference(superposition,[],[f18093,f279]) ).
fof(f18093,plain,
( ! [X1] : is_a_theorem(implies(X1,not(not(X1))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f18092]) ).
fof(f18092,plain,
( spl1_3
<=> ! [X1] : is_a_theorem(implies(X1,not(not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f119304,plain,
( ! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| not(not(X0)) = X0 )
| ~ spl1_3 ),
inference(forward_demodulation,[],[f118930,f279]) ).
fof(f118930,plain,
( ! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| not(not(X0)) = X0 )
| ~ spl1_3 ),
inference(resolution,[],[f5570,f18093]) ).
fof(f98973,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97476]) ).
fof(f97476,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f701]) ).
fof(f701,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f354,f231]) ).
fof(f354,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f238,f242]) ).
fof(f18096,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f18095]) ).
fof(f18095,plain,
( spl1_4
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f98972,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97480]) ).
fof(f97480,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f231]) ).
fof(f98971,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97481]) ).
fof(f97481,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92490]) ).
fof(f92490,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[],[f10237,f235]) ).
fof(f10237,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(equiv(X2,X2),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f9803,f8111]) ).
fof(f8111,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5901,f242]) ).
fof(f5901,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f1689,f231]) ).
fof(f1689,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f695,f242]) ).
fof(f695,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(f9803,plain,
! [X0,X1] : is_a_theorem(implies(implies(equiv(X0,X0),X1),X1)),
inference(resolution,[],[f9789,f1685]) ).
fof(f1685,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[],[f695,f354]) ).
fof(f9789,plain,
! [X0,X1] : is_a_theorem(implies(X0,equiv(X1,X1))),
inference(subsumption_resolution,[],[f9683,f701]) ).
fof(f9683,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,equiv(X1,X1)))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(resolution,[],[f8111,f705]) ).
fof(f705,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f354,f240]) ).
fof(f98970,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97487]) ).
fof(f97487,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92500]) ).
fof(f92500,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,equiv(X2,X2)))),
inference(resolution,[],[f10237,f231]) ).
fof(f98969,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97488]) ).
fof(f97488,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f234]) ).
fof(f98968,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97490]) ).
fof(f97490,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20954]) ).
fof(f20954,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(necessarily(not(X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19285,f322]) ).
fof(f322,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f318,f242]) ).
fof(f19285,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(X0),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19268,f6062]) ).
fof(f6062,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,necessarily(X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f6061,f279]) ).
fof(f6061,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,necessarily(X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5944,f279]) ).
fof(f5944,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f225]) ).
fof(f19268,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0))
| ~ spl1_3 ),
inference(superposition,[],[f18291,f219]) ).
fof(f18291,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18238,f8246]) ).
fof(f8246,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f8243,f279]) ).
fof(f8243,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5928,f279]) ).
fof(f5928,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f232]) ).
fof(f98967,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97491]) ).
fof(f97491,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24906]) ).
fof(f24906,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(necessarily(necessarily(not(X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20958,f322]) ).
fof(f20958,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(necessarily(X0)),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19285,f6062]) ).
fof(f98966,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97492]) ).
fof(f97492,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23540]) ).
fof(f23540,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(and(X1,not(X0)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f19283,f322]) ).
fof(f19283,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,X1),X2),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19268,f8827]) ).
fof(f8827,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X0,X2)) ),
inference(forward_demodulation,[],[f8824,f279]) ).
fof(f8824,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(not(X0),X2)) ),
inference(superposition,[],[f5929,f279]) ).
fof(f5929,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X2,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f233]) ).
fof(f98965,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97493]) ).
fof(f97493,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23560]) ).
fof(f23560,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(and(not(X0),X1),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f322]) ).
fof(f19284,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,X1),X2),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19268,f8246]) ).
fof(f98964,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97494]) ).
fof(f97494,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9789]) ).
fof(f98963,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97497]) ).
fof(f97497,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18093]) ).
fof(f98962,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97500]) ).
fof(f97500,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f27576]) ).
fof(f27576,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(not(equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f18619,f298]) ).
fof(f298,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(superposition,[],[f231,f279]) ).
fof(f18619,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(not(equiv(X1,X1)),X0))
| is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18113,f1645]) ).
fof(f1645,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f1594,f279]) ).
fof(f1594,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1001,f1254]) ).
fof(f1254,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1137,f374]) ).
fof(f374,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f258,f291]) ).
fof(f291,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X0),X1),
inference(superposition,[],[f218,f279]) ).
fof(f258,plain,
! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f242,f225]) ).
fof(f1137,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1100,f291]) ).
fof(f1100,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f919,f230]) ).
fof(f919,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f792,f247]) ).
fof(f792,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f551,f242]) ).
fof(f551,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f505,f242]) ).
fof(f505,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))),
inference(forward_demodulation,[],[f239,f218]) ).
fof(f1001,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f916,f242]) ).
fof(f916,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f758,f242]) ).
fof(f758,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(resolution,[],[f244,f354]) ).
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(f18113,plain,
( ! [X0] : is_a_theorem(necessarily(not(not(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f10235]) ).
fof(f10235,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f9803,f5839]) ).
fof(f5839,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5791,f247]) ).
fof(f5791,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f5782,f218]) ).
fof(f5782,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f5767,f919]) ).
fof(f5767,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1685,f252]) ).
fof(f252,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f242,f231]) ).
fof(f98961,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97501]) ).
fof(f97501,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28245]) ).
fof(f28245,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f19121,f298]) ).
fof(f19121,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(not(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18117,f1645]) ).
fof(f18117,plain,
( ! [X0] : is_a_theorem(necessarily(not(not(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f10258]) ).
fof(f10258,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(strict_equiv(X1,X1),X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f9815,f5839]) ).
fof(f9815,plain,
! [X0,X1] : is_a_theorem(implies(implies(strict_equiv(X0,X0),X1),X1)),
inference(resolution,[],[f9791,f1685]) ).
fof(f9791,plain,
! [X0,X1] : is_a_theorem(implies(X0,strict_equiv(X1,X1))),
inference(subsumption_resolution,[],[f9773,f1888]) ).
fof(f1888,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f1842,f716]) ).
fof(f716,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[],[f701,f279]) ).
fof(f1842,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1155,f376]) ).
fof(f376,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f228,f291]) ).
fof(f1155,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(forward_demodulation,[],[f1154,f218]) ).
fof(f1154,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(forward_demodulation,[],[f1115,f291]) ).
fof(f1115,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,not(X1))))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f919,f318]) ).
fof(f9773,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,strict_equiv(X1,X1)))
| ~ is_a_theorem(strict_implies(X1,X1)) ),
inference(resolution,[],[f8111,f727]) ).
fof(f727,plain,
! [X0] : is_a_theorem(implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(superposition,[],[f702,f220]) ).
fof(f702,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f354,f234]) ).
fof(f98960,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97502]) ).
fof(f97502,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19254]) ).
fof(f19254,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(not(X0),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f322]) ).
fof(f98959,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97503]) ).
fof(f97503,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23032]) ).
fof(f23032,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(X1,necessarily(not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f19163,f322]) ).
fof(f19163,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,necessarily(X1))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f6062]) ).
fof(f18290,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,X1)),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18238,f8827]) ).
fof(f98958,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97504]) ).
fof(f97504,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23215]) ).
fof(f23215,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(necessarily(not(X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19258,f322]) ).
fof(f19258,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(necessarily(X0),X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f6062]) ).
fof(f98957,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97505]) ).
fof(f97505,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20187]) ).
fof(f20187,plain,
( ! [X0] : is_a_theorem(implies(X0,not(necessarily(necessarily(not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18398,f322]) ).
fof(f18398,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(X0))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18292,f6062]) ).
fof(f18292,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(X0)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18238,f6062]) ).
fof(f98956,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97506]) ).
fof(f97506,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23700]) ).
fof(f23700,plain,
( ! [X0] : is_a_theorem(implies(X0,not(necessarily(necessarily(necessarily(not(X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20191,f322]) ).
fof(f20191,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(necessarily(X0)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18398,f6062]) ).
fof(f98955,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97507]) ).
fof(f97507,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f22641]) ).
fof(f22641,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(necessarily(and(X1,not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18396,f322]) ).
fof(f18396,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,X1))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18292,f8827]) ).
fof(f98954,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97508]) ).
fof(f97508,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f22660]) ).
fof(f22660,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(necessarily(and(not(X0),X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f322]) ).
fof(f18397,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,X1))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18292,f8246]) ).
fof(f98953,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97509]) ).
fof(f97509,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f702]) ).
fof(f98952,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97512]) ).
fof(f97512,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10385]) ).
fof(f10385,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),X0))),
inference(resolution,[],[f9818,f234]) ).
fof(f9818,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f9804,f1001]) ).
fof(f9804,plain,
! [X0,X1] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[],[f9789,f279]) ).
fof(f98951,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97513]) ).
fof(f97513,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10689]) ).
fof(f10689,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(strict_equiv(X1,X1),X0))),
inference(resolution,[],[f9835,f234]) ).
fof(f9835,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(strict_equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f9816,f1001]) ).
fof(f9816,plain,
! [X0,X1] : is_a_theorem(or(X0,strict_equiv(X1,X1))),
inference(superposition,[],[f9791,f279]) ).
fof(f98950,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97515]) ).
fof(f97515,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f14430]) ).
fof(f14430,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(possibly(equiv(X1,X1)),X0))),
inference(resolution,[],[f11748,f234]) ).
fof(f11748,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f11716,f1001]) ).
fof(f11716,plain,
! [X0,X1] : is_a_theorem(or(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f11687,f6442]) ).
fof(f6442,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f6062,f1170]) ).
fof(f1170,plain,
! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1133,f374]) ).
fof(f1133,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1094,f218]) ).
fof(f1094,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f919,f231]) ).
fof(f11687,plain,
! [X0] : is_a_theorem(necessarily(necessarily(possibly(equiv(X0,X0))))),
inference(resolution,[],[f10235,f226]) ).
fof(f98949,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97516]) ).
fof(f97516,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f14883]) ).
fof(f14883,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(possibly(strict_equiv(X1,X1)),X0))),
inference(resolution,[],[f12130,f234]) ).
fof(f12130,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f12098,f1001]) ).
fof(f12098,plain,
! [X0,X1] : is_a_theorem(or(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12072,f6442]) ).
fof(f12072,plain,
! [X0] : is_a_theorem(necessarily(necessarily(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f10258,f226]) ).
fof(f98948,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97525]) ).
fof(f97525,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11961]) ).
fof(f11961,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),possibly(X0)))),
inference(forward_demodulation,[],[f11942,f221]) ).
fof(f11942,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),not(necessarily(not(X0)))))),
inference(resolution,[],[f10242,f1299]) ).
fof(f1299,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),not(X2)))
| is_a_theorem(implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f322,f284]) ).
fof(f284,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f274,f219]) ).
fof(f274,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f222,f219]) ).
fof(f10242,plain,
! [X0,X1] : is_a_theorem(implies(implies(equiv(X0,X0),necessarily(X1)),X1)),
inference(resolution,[],[f9803,f5944]) ).
fof(f98947,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97526]) ).
fof(f97526,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12270]) ).
fof(f12270,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(strict_equiv(X1,X1),possibly(X0)))),
inference(forward_demodulation,[],[f12251,f221]) ).
fof(f12251,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(strict_equiv(X1,X1),not(necessarily(not(X0)))))),
inference(resolution,[],[f10265,f1299]) ).
fof(f10265,plain,
! [X0,X1] : is_a_theorem(implies(implies(strict_equiv(X0,X0),necessarily(X1)),X1)),
inference(resolution,[],[f9815,f5944]) ).
fof(f98946,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97527]) ).
fof(f97527,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f229]) ).
fof(f98945,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97532]) ).
fof(f97532,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92545]) ).
fof(f92545,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(X1,equiv(X2,X2)))),
inference(resolution,[],[f10237,f229]) ).
fof(f98944,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97533]) ).
fof(f97533,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92492]) ).
fof(f92492,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,not(X1)))),
inference(resolution,[],[f10237,f293]) ).
fof(f293,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X1,not(X0)),or(X0,X1))),
inference(superposition,[],[f235,f279]) ).
fof(f98943,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97534]) ).
fof(f97534,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f301]) ).
fof(f301,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,and(X1,not(X0))))),
inference(superposition,[],[f234,f279]) ).
fof(f98942,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97535]) ).
fof(f97535,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f230]) ).
fof(f98941,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97536]) ).
fof(f97536,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92551]) ).
fof(f92551,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(equiv(X1,X1),X2))),
inference(resolution,[],[f10237,f230]) ).
fof(f98940,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97537]) ).
fof(f97537,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f226]) ).
fof(f98939,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97541]) ).
fof(f97541,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92552]) ).
fof(f92552,plain,
! [X0,X1] : is_a_theorem(implies(X0,necessarily(possibly(equiv(X1,X1))))),
inference(resolution,[],[f10237,f226]) ).
fof(f98938,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97545]) ).
fof(f97545,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45615]) ).
fof(f45615,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41532,f3750]) ).
fof(f3750,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1653,f1861]) ).
fof(f1861,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f1845,f228]) ).
fof(f1845,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1155,f1133]) ).
fof(f1653,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1627,f291]) ).
fof(f1627,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(or(X1,not(X0)))) ),
inference(resolution,[],[f1594,f318]) ).
fof(f41532,plain,
( ! [X0,X1] : is_a_theorem(not(not(strict_implies(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(superposition,[],[f32252,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(f32252,plain,
( ! [X0,X1] : is_a_theorem(not(possibly(and(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f23103,f18154]) ).
fof(f18154,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(not(possibly(X0))) )
| ~ spl1_3 ),
inference(superposition,[],[f18098,f221]) ).
fof(f18098,plain,
( ! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18093,f242]) ).
fof(f23103,plain,
( ! [X0,X1] : is_a_theorem(necessarily(not(and(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f10245]) ).
fof(f10245,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(equiv(X0,X0),X1))
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f10231,f218]) ).
fof(f10231,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(equiv(X0,X0),X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f9803,f919]) ).
fof(f19253,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(not(X0),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f1842]) ).
fof(f98937,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97546]) ).
fof(f97546,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45645]) ).
fof(f45645,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41560,f3750]) ).
fof(f41560,plain,
( ! [X0,X1] : is_a_theorem(not(not(strict_implies(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(superposition,[],[f32327,f266]) ).
fof(f32327,plain,
( ! [X0,X1] : is_a_theorem(not(possibly(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f23111,f18154]) ).
fof(f23111,plain,
( ! [X0,X1] : is_a_theorem(necessarily(not(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f10268]) ).
fof(f10268,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(strict_equiv(X0,X0),X1))
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f10254,f218]) ).
fof(f10254,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(strict_equiv(X0,X0),X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f9815,f919]) ).
fof(f98936,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97549]) ).
fof(f97549,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9791]) ).
fof(f98935,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97550]) ).
fof(f97550,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6035]) ).
fof(f6035,plain,
! [X0] : is_a_theorem(implies(X0,possibly(X0))),
inference(resolution,[],[f5944,f226]) ).
fof(f98934,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97554]) ).
fof(f97554,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11717]) ).
fof(f11717,plain,
! [X0,X1] : is_a_theorem(implies(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f11687,f6038]) ).
fof(f6038,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f5944,f1169]) ).
fof(f1169,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1133,f261]) ).
fof(f261,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f258,f218]) ).
fof(f98933,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97555]) ).
fof(f97555,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12099]) ).
fof(f12099,plain,
! [X0,X1] : is_a_theorem(implies(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12072,f6038]) ).
fof(f98932,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97564]) ).
fof(f97564,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f238]) ).
fof(f98931,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97565]) ).
fof(f97565,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f240]) ).
fof(f98930,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97566]) ).
fof(f97566,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f243]) ).
fof(f98929,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97567]) ).
fof(f97567,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f244]) ).
fof(f98928,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97571]) ).
fof(f97571,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f758]) ).
fof(f98927,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97573]) ).
fof(f97573,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f762]) ).
fof(f762,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X1),implies(or(X0,X1),implies(or(X2,not(X0)),X1)))),
inference(superposition,[],[f244,f279]) ).
fof(f98926,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97575]) ).
fof(f97575,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f697]) ).
fof(f697,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,not(X0)),implies(or(X0,X1),implies(X2,X1)))),
inference(superposition,[],[f243,f279]) ).
fof(f98925,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97576]) ).
fof(f97576,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f577]) ).
fof(f577,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,not(X0)),implies(or(X0,X1),equiv(X1,not(X0))))),
inference(superposition,[],[f240,f279]) ).
fof(f98924,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97577]) ).
fof(f97577,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f705]) ).
fof(f98923,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97579]) ).
fof(f97579,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2714]) ).
fof(f2714,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,f281]) ).
fof(f281,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
inference(superposition,[],[f219,f222]) ).
fof(f98922,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97581]) ).
fof(f97581,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2777]) ).
fof(f2777,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,[],[f2776,f281]) ).
fof(f2776,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,[],[f2719,f279]) ).
fof(f2719,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,f281]) ).
fof(f98921,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97582]) ).
fof(f97582,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2061]) ).
fof(f2061,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,[],[f324,f284]) ).
fof(f324,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,X1)),implies(and(X0,not(X1)),X2))),
inference(superposition,[],[f318,f219]) ).
fof(f98920,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97583]) ).
fof(f97583,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1300]) ).
fof(f1300,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X2,and(X0,not(X1))))),
inference(superposition,[],[f318,f284]) ).
fof(f98919,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97584]) ).
fof(f97584,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3027]) ).
fof(f3027,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,[],[f325,f284]) ).
fof(f325,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,X1)),implies(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f318,f222]) ).
fof(f98918,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97585]) ).
fof(f97585,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1315]) ).
fof(f1315,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),possibly(X2)),implies(necessarily(not(X2)),and(X0,not(X1))))),
inference(superposition,[],[f323,f284]) ).
fof(f323,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,possibly(X0)),implies(necessarily(not(X0)),X1))),
inference(superposition,[],[f318,f221]) ).
fof(f98917,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97587]) ).
fof(f97587,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9803]) ).
fof(f98916,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97588]) ).
fof(f97588,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10242]) ).
fof(f98915,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97589]) ).
fof(f97589,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1282]) ).
fof(f1282,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,f284]) ).
fof(f98914,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97590]) ).
fof(f97590,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1923]) ).
fof(f1923,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,f285]) ).
fof(f285,plain,
! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(forward_demodulation,[],[f275,f219]) ).
fof(f275,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),X2) = not(and(or(X0,X1),not(X2))),
inference(superposition,[],[f222,f222]) ).
fof(f98913,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97592]) ).
fof(f97592,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2774]) ).
fof(f2774,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,[],[f2716,f279]) ).
fof(f2716,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,f281]) ).
fof(f98912,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97593]) ).
fof(f97593,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2813]) ).
fof(f2813,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,[],[f2812,f279]) ).
fof(f2812,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,[],[f2756,f284]) ).
fof(f2756,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,[],[f324,f281]) ).
fof(f98911,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97594]) ).
fof(f97594,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2794]) ).
fof(f2794,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X1,X2),not(X0)),not(and(X0,or(X1,X2))))),
inference(forward_demodulation,[],[f2793,f279]) ).
fof(f2793,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(not(X1),X2),not(X0)),not(and(X0,or(X1,X2))))),
inference(forward_demodulation,[],[f2727,f284]) ).
fof(f2727,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(and(not(X1),not(X2)),not(X0)),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f318,f281]) ).
fof(f98910,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97595]) ).
fof(f97595,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3052]) ).
fof(f3052,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,[],[f3028,f281]) ).
fof(f3028,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,[],[f325,f285]) ).
fof(f98909,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97596]) ).
fof(f97596,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2823]) ).
fof(f2823,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,[],[f2822,f279]) ).
fof(f2822,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,[],[f2763,f284]) ).
fof(f2763,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,[],[f323,f281]) ).
fof(f98908,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97599]) ).
fof(f97599,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f763]) ).
fof(f763,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,f283]) ).
fof(f283,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(forward_demodulation,[],[f273,f219]) ).
fof(f273,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = not(and(possibly(X0),not(X1))),
inference(superposition,[],[f222,f221]) ).
fof(f98907,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97601]) ).
fof(f97601,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9815]) ).
fof(f98906,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97602]) ).
fof(f97602,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10265]) ).
fof(f98905,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97603]) ).
fof(f97603,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2060]) ).
fof(f2060,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(possibly(X0),implies(X1,X2)),implies(and(X1,not(X2)),necessarily(not(X0))))),
inference(superposition,[],[f324,f283]) ).
fof(f98904,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97604]) ).
fof(f97604,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f638]) ).
fof(f638,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),not(X1)),implies(X1,necessarily(not(X0))))),
inference(superposition,[],[f318,f283]) ).
fof(f98903,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97605]) ).
fof(f97605,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3026]) ).
fof(f3026,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,[],[f325,f283]) ).
fof(f98902,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97606]) ).
fof(f97606,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f941]) ).
fof(f941,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),possibly(X1)),implies(necessarily(not(X1)),necessarily(not(X0))))),
inference(superposition,[],[f323,f283]) ).
fof(f98901,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97608]) ).
fof(f97608,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11773]) ).
fof(f11773,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(equiv(X0,X0)),X1),X1)),
inference(resolution,[],[f11717,f1685]) ).
fof(f98900,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97609]) ).
fof(f97609,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12155]) ).
fof(f12155,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(strict_equiv(X0,X0)),X1),X1)),
inference(resolution,[],[f12099,f1685]) ).
fof(f98899,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97610]) ).
fof(f97610,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f235]) ).
fof(f98898,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97611]) ).
fof(f97611,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f236]) ).
fof(f98897,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97612]) ).
fof(f97612,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f293]) ).
fof(f98896,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97613]) ).
fof(f97613,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2713]) ).
fof(f2713,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X0,and(not(X1),not(X2))),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f236,f281]) ).
fof(f98895,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97614]) ).
fof(f97614,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f294]) ).
fof(f294,plain,
! [X0,X1] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f236,f279]) ).
fof(f98894,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97615]) ).
fof(f97615,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2712]) ).
fof(f2712,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(and(not(X1),not(X2)),X0),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f235,f281]) ).
fof(f98893,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97616]) ).
fof(f97616,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f232]) ).
fof(f98892,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97617]) ).
fof(f97617,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f233]) ).
fof(f98891,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97620]) ).
fof(f97620,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8309]) ).
fof(f8309,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,equiv(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f8216,f223]) ).
fof(f8216,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,X2)),X1)),
inference(resolution,[],[f5928,f233]) ).
fof(f98890,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97621]) ).
fof(f97621,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8933]) ).
fof(f8933,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,equiv(X0,X1)),implies(X1,X0))),
inference(superposition,[],[f8784,f223]) ).
fof(f8784,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,X2)),X2)),
inference(resolution,[],[f5929,f233]) ).
fof(f98889,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97624]) ).
fof(f97624,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1281]) ).
fof(f1281,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(X1)),implies(implies(X0,X1),X2))),
inference(superposition,[],[f230,f284]) ).
fof(f98888,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97625]) ).
fof(f97625,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f7826]) ).
fof(f7826,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(equiv(X0,X1)))),
inference(superposition,[],[f1281,f1706]) ).
fof(f1706,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(f98887,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97626]) ).
fof(f97626,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f7831]) ).
fof(f7831,plain,
! [X0,X1] : is_a_theorem(implies(and(X1,not(X0)),not(equiv(X0,X1)))),
inference(superposition,[],[f231,f1706]) ).
fof(f98886,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97627]) ).
fof(f97627,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6045]) ).
fof(f6045,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(strict_implies(X0,X1)))),
inference(resolution,[],[f5944,f583]) ).
fof(f583,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),necessarily(not(strict_implies(X0,X1))))),
inference(superposition,[],[f226,f266]) ).
fof(f98885,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97628]) ).
fof(f97628,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18129]) ).
fof(f18129,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(implies(X0,X1))))
| ~ spl1_3 ),
inference(superposition,[],[f18093,f219]) ).
fof(f98884,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97629]) ).
fof(f97629,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f583]) ).
fof(f98883,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97630]) ).
fof(f97630,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28202]) ).
fof(f28202,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(equiv(X1,X1))),X2))
| ~ spl1_3 ),
inference(resolution,[],[f18622,f19283]) ).
fof(f18622,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,not(equiv(X1,X1))))
| is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18113,f2938]) ).
fof(f2938,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X1)))
| is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f2922,f1434]) ).
fof(f1434,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1416,f242]) ).
fof(f1416,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1134,f261]) ).
fof(f1134,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,and(X0,X1)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1095,f218]) ).
fof(f1095,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(implies(X1,and(X0,X1)))) ),
inference(resolution,[],[f919,f234]) ).
fof(f2922,plain,
! [X0,X1] :
( ~ is_a_theorem(and(not(X1),or(X0,X1)))
| is_a_theorem(X0) ),
inference(resolution,[],[f2886,f242]) ).
fof(f2886,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),or(X1,X0)),X1)),
inference(resolution,[],[f2771,f322]) ).
fof(f2771,plain,
! [X0,X1] : is_a_theorem(or(X1,not(and(not(X0),or(X1,X0))))),
inference(forward_demodulation,[],[f2702,f279]) ).
fof(f2702,plain,
! [X0,X1] : is_a_theorem(implies(not(X1),not(and(not(X0),or(X1,X0))))),
inference(superposition,[],[f234,f281]) ).
fof(f98882,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97631]) ).
fof(f97631,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28451]) ).
fof(f28451,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(strict_equiv(X1,X1))),X2))
| ~ spl1_3 ),
inference(resolution,[],[f19124,f19283]) ).
fof(f19124,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,not(strict_equiv(X1,X1))))
| is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18117,f2938]) ).
fof(f98881,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97632]) ).
fof(f97632,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8216]) ).
fof(f98880,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97633]) ).
fof(f97633,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8307]) ).
fof(f8307,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(necessarily(X1),X2)),X1)),
inference(resolution,[],[f8216,f5944]) ).
fof(f98879,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97634]) ).
fof(f97634,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8487]) ).
fof(f8487,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(necessarily(necessarily(X1)),X2)),X1)),
inference(resolution,[],[f8307,f5944]) ).
fof(f98878,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97635]) ).
fof(f97635,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8784]) ).
fof(f98877,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97636]) ).
fof(f97636,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8304]) ).
fof(f8304,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(and(X1,X2),X3)),X1)),
inference(resolution,[],[f8216,f5928]) ).
fof(f98876,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97637]) ).
fof(f97637,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8786]) ).
fof(f8786,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(and(X1,X2),X3)),X2)),
inference(resolution,[],[f5929,f8216]) ).
fof(f98875,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97638]) ).
fof(f97638,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8927]) ).
fof(f8927,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(X1,and(X2,X3))),X3)),
inference(resolution,[],[f8784,f5929]) ).
fof(f98874,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97639]) ).
fof(f97639,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8928]) ).
fof(f8928,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(X1,and(X2,X3))),X2)),
inference(resolution,[],[f8784,f5928]) ).
fof(f98873,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97640]) ).
fof(f97640,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8931]) ).
fof(f8931,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,necessarily(X2))),X2)),
inference(resolution,[],[f8784,f5944]) ).
fof(f98872,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97641]) ).
fof(f97641,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9194]) ).
fof(f9194,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,necessarily(necessarily(X2)))),X2)),
inference(resolution,[],[f8931,f5944]) ).
fof(f98871,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97642]) ).
fof(f97642,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6044]) ).
fof(f6044,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(X1)),X1)),
inference(resolution,[],[f5944,f233]) ).
fof(f98870,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97643]) ).
fof(f97643,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f31852]) ).
fof(f31852,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(not(not(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f23031,f1653]) ).
fof(f23031,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(X1,necessarily(not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f19163,f1842]) ).
fof(f98869,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97644]) ).
fof(f97644,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8218]) ).
fof(f8218,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,X2))),X1)),
inference(resolution,[],[f5928,f6044]) ).
fof(f98868,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97645]) ).
fof(f97645,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8392]) ).
fof(f8392,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(necessarily(X1),X2))),X1)),
inference(resolution,[],[f8218,f5944]) ).
fof(f98867,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97646]) ).
fof(f97646,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6127]) ).
fof(f6127,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(X1))),X1)),
inference(resolution,[],[f6044,f5944]) ).
fof(f98866,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97647]) ).
fof(f97647,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6200]) ).
fof(f6200,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(necessarily(X1)))),X1)),
inference(resolution,[],[f6127,f5944]) ).
fof(f98865,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97648]) ).
fof(f97648,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50239]) ).
fof(f50239,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6072,f6127]) ).
fof(f6072,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(necessarily(X1))))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f6052,f1689]) ).
fof(f6052,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(X0)),X0)),
inference(resolution,[],[f5944,f225]) ).
fof(f98864,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97649]) ).
fof(f97649,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8219]) ).
fof(f8219,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(and(X1,X2)))),X1)),
inference(resolution,[],[f5928,f6127]) ).
fof(f98863,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97650]) ).
fof(f97650,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8788]) ).
fof(f8788,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,X2))),X2)),
inference(resolution,[],[f5929,f6044]) ).
fof(f98862,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97651]) ).
fof(f97651,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9019]) ).
fof(f9019,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,necessarily(X2)))),X2)),
inference(resolution,[],[f8788,f5944]) ).
fof(f98861,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97652]) ).
fof(f97652,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8789]) ).
fof(f8789,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(and(X1,X2)))),X2)),
inference(resolution,[],[f5929,f6127]) ).
fof(f98860,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97653]) ).
fof(f97653,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6128]) ).
fof(f6128,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,strict_implies(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f6044,f218]) ).
fof(f98859,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97654]) ).
fof(f97654,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8308]) ).
fof(f8308,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,strict_equiv(X0,X1)),strict_implies(X0,X1))),
inference(superposition,[],[f8216,f220]) ).
fof(f98858,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97655]) ).
fof(f97655,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8932]) ).
fof(f8932,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,strict_equiv(X0,X1)),strict_implies(X1,X0))),
inference(superposition,[],[f8784,f220]) ).
fof(f98857,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97656]) ).
fof(f97656,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8292]) ).
fof(f8292,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(equiv(X0,X1),X2),implies(X0,X1))),
inference(superposition,[],[f8215,f223]) ).
fof(f8215,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,X1),X2),X0)),
inference(resolution,[],[f5928,f232]) ).
fof(f98856,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97657]) ).
fof(f97657,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8915]) ).
fof(f8915,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(equiv(X0,X1),X2),implies(X1,X0))),
inference(superposition,[],[f8783,f223]) ).
fof(f8783,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,X1),X2),X1)),
inference(resolution,[],[f5929,f232]) ).
fof(f98855,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97658]) ).
fof(f97658,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2886]) ).
fof(f98854,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97659]) ).
fof(f97659,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6046]) ).
fof(f6046,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),or(necessarily(X1),X0)),X1)),
inference(resolution,[],[f5944,f2886]) ).
fof(f98853,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97662]) ).
fof(f97662,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1922]) ).
fof(f1922,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2))),
inference(superposition,[],[f230,f285]) ).
fof(f98852,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97663]) ).
fof(f97663,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2711]) ).
fof(f2711,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(not(X1),not(X2)),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f231,f281]) ).
fof(f98851,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97664]) ).
fof(f97664,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28203]) ).
fof(f28203,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(not(equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f18622,f19284]) ).
fof(f98850,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97665]) ).
fof(f97665,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23105]) ).
fof(f23105,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(not(X0)),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f1653]) ).
fof(f98849,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97666]) ).
fof(f97666,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24540]) ).
fof(f24540,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(not(necessarily(X0))),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23105,f5944]) ).
fof(f98848,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97667]) ).
fof(f97667,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28452]) ).
fof(f28452,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f19124,f19284]) ).
fof(f98847,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97668]) ).
fof(f97668,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f39263]) ).
fof(f39263,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(possibly(X0)),X1),not(X0)))
| ~ spl1_3 ),
inference(superposition,[],[f24540,f221]) ).
fof(f98846,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97669]) ).
fof(f97669,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8215]) ).
fof(f98845,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97670]) ).
fof(f97670,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8290]) ).
fof(f8290,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(necessarily(X0),X1),X2),X0)),
inference(resolution,[],[f8215,f5944]) ).
fof(f98844,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97671]) ).
fof(f97671,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8472]) ).
fof(f8472,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(necessarily(necessarily(X0)),X1),X2),X0)),
inference(resolution,[],[f8290,f5944]) ).
fof(f98843,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97672]) ).
fof(f97672,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8783]) ).
fof(f98842,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97673]) ).
fof(f97673,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8913]) ).
fof(f8913,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,necessarily(X1)),X2),X1)),
inference(resolution,[],[f8783,f5944]) ).
fof(f98841,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97674]) ).
fof(f97674,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9178]) ).
fof(f9178,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,necessarily(necessarily(X1))),X2),X1)),
inference(resolution,[],[f8913,f5944]) ).
fof(f98840,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97675]) ).
fof(f97675,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8287]) ).
fof(f8287,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(and(X0,X1),X2),X3),X0)),
inference(resolution,[],[f8215,f5928]) ).
fof(f98839,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97676]) ).
fof(f97676,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8793]) ).
fof(f8793,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(and(X0,X1),X2),X3),X1)),
inference(resolution,[],[f5929,f8215]) ).
fof(f98838,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97677]) ).
fof(f97677,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8909]) ).
fof(f8909,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(X0,and(X1,X2)),X3),X2)),
inference(resolution,[],[f8783,f5929]) ).
fof(f98837,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97678]) ).
fof(f97678,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8910]) ).
fof(f8910,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(X0,and(X1,X2)),X3),X1)),
inference(resolution,[],[f8783,f5928]) ).
fof(f98836,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97679]) ).
fof(f97679,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6043]) ).
fof(f6043,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(X0),X1),X0)),
inference(resolution,[],[f5944,f232]) ).
fof(f98835,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97680]) ).
fof(f97680,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6116]) ).
fof(f6116,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(X0)),X1),X0)),
inference(resolution,[],[f6043,f5944]) ).
fof(f98834,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97681]) ).
fof(f97681,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6189]) ).
fof(f6189,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(necessarily(X0))),X1),X0)),
inference(resolution,[],[f6116,f5944]) ).
fof(f98833,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97682]) ).
fof(f97682,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50255]) ).
fof(f50255,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(necessarily(necessarily(X0)))),X1),X0)),
inference(resolution,[],[f6072,f6116]) ).
fof(f98832,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97683]) ).
fof(f97683,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f32572]) ).
fof(f32572,plain,
( ! [X0,X1] : is_a_theorem(implies(and(necessarily(not(not(X0))),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23214,f1653]) ).
fof(f23214,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(necessarily(not(X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19258,f1842]) ).
fof(f98831,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97684]) ).
fof(f97684,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8222]) ).
fof(f8222,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,X1)),X2),X0)),
inference(resolution,[],[f5928,f6043]) ).
fof(f98830,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97685]) ).
fof(f97685,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8409]) ).
fof(f8409,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(necessarily(X0),X1)),X2),X0)),
inference(resolution,[],[f8222,f5944]) ).
fof(f98829,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97686]) ).
fof(f97686,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8223]) ).
fof(f8223,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(and(X0,X1))),X2),X0)),
inference(resolution,[],[f5928,f6116]) ).
fof(f98828,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97687]) ).
fof(f97687,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8795]) ).
fof(f8795,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,X1)),X2),X1)),
inference(resolution,[],[f5929,f6043]) ).
fof(f98827,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97688]) ).
fof(f97688,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9037]) ).
fof(f9037,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,necessarily(X1))),X2),X1)),
inference(resolution,[],[f8795,f5944]) ).
fof(f98826,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97689]) ).
fof(f97689,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8796]) ).
fof(f8796,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(and(X0,X1))),X2),X1)),
inference(resolution,[],[f5929,f6116]) ).
fof(f98825,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97690]) ).
fof(f97690,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6117]) ).
fof(f6117,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(strict_implies(X0,X1),X2),implies(X0,X1))),
inference(superposition,[],[f6043,f218]) ).
fof(f98824,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97691]) ).
fof(f97691,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8291]) ).
fof(f8291,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(strict_equiv(X0,X1),X2),strict_implies(X0,X1))),
inference(superposition,[],[f8215,f220]) ).
fof(f98823,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97692]) ).
fof(f97692,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8914]) ).
fof(f8914,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(strict_equiv(X0,X1),X2),strict_implies(X1,X0))),
inference(superposition,[],[f8783,f220]) ).
fof(f98822,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97700]) ).
fof(f97700,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f699]) ).
fof(f699,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))),
inference(forward_demodulation,[],[f696,f279]) ).
fof(f696,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X0),X2)))),
inference(superposition,[],[f243,f279]) ).
fof(f98821,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97701]) ).
fof(f97701,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f576]) ).
fof(f576,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,not(X0)),equiv(not(X0),X1)))),
inference(superposition,[],[f240,f279]) ).
fof(f98820,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97702]) ).
fof(f97702,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f761]) ).
fof(f761,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X2,X1),implies(or(not(X0),X2),X1)))),
inference(superposition,[],[f244,f279]) ).
fof(f98819,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97706]) ).
fof(f97706,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f324]) ).
fof(f98818,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97707]) ).
fof(f97707,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f823]) ).
fof(f823,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,necessarily(not(X1)))),implies(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f318,f263]) ).
fof(f263,plain,
! [X0,X1] : implies(X1,necessarily(not(X0))) = not(and(X1,possibly(X0))),
inference(superposition,[],[f219,f221]) ).
fof(f98817,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97708]) ).
fof(f97708,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1734]) ).
fof(f1734,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,[],[f318,f264]) ).
fof(f98816,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97709]) ).
fof(f97709,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2066]) ).
fof(f2066,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,[],[f324,f263]) ).
fof(f98815,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97710]) ).
fof(f97710,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2068]) ).
fof(f2068,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,[],[f324,f264]) ).
fof(f98814,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97711]) ).
fof(f97711,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2067]) ).
fof(f2067,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,[],[f324,f276]) ).
fof(f276,plain,
! [X0,X1] : or(X1,necessarily(not(X0))) = not(and(not(X1),possibly(X0))),
inference(superposition,[],[f222,f221]) ).
fof(f98813,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97712]) ).
fof(f97712,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2429]) ).
fof(f2429,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,[],[f324,f277]) ).
fof(f277,plain,
! [X2,X0,X1] : or(X2,and(X0,not(X1))) = not(and(not(X2),implies(X0,X1))),
inference(superposition,[],[f222,f219]) ).
fof(f98812,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97713]) ).
fof(f97713,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f318]) ).
fof(f98811,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97714]) ).
fof(f97714,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f326]) ).
fof(f98810,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97715]) ).
fof(f97715,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f757]) ).
fof(f757,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),equiv(not(X0),not(X0)))),
inference(superposition,[],[f705,f279]) ).
fof(f98809,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97716]) ).
fof(f97716,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f357]) ).
fof(f357,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[],[f355,f279]) ).
fof(f355,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,implies(not(X0),X1)),implies(not(X0),X1))),
inference(superposition,[],[f238,f279]) ).
fof(f98808,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97717]) ).
fof(f97717,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f325]) ).
fof(f98807,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97718]) ).
fof(f97718,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1036]) ).
fof(f1036,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,necessarily(not(X1)))),implies(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f318,f276]) ).
fof(f98806,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97719]) ).
fof(f97719,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2426]) ).
fof(f2426,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,[],[f318,f277]) ).
fof(f98805,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97720]) ).
fof(f97720,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3038]) ).
fof(f3038,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,[],[f325,f222]) ).
fof(f98804,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97721]) ).
fof(f97721,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3039]) ).
fof(f3039,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,[],[f325,f263]) ).
fof(f98803,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97722]) ).
fof(f97722,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3040]) ).
fof(f3040,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,[],[f325,f276]) ).
fof(f98802,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97723]) ).
fof(f97723,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3041]) ).
fof(f3041,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,[],[f325,f264]) ).
fof(f98801,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97724]) ).
fof(f97724,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3032]) ).
fof(f3032,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,[],[f325,f263]) ).
fof(f98800,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97725]) ).
fof(f97725,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3034]) ).
fof(f3034,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,[],[f325,f264]) ).
fof(f98799,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97727]) ).
fof(f97727,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f323]) ).
fof(f98798,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97728]) ).
fof(f97728,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f954]) ).
fof(f954,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,[],[f945,f218]) ).
fof(f945,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,[],[f323,f263]) ).
fof(f98797,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97729]) ).
fof(f97729,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1784]) ).
fof(f1784,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,[],[f1736,f218]) ).
fof(f1736,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,[],[f323,f264]) ).
fof(f98796,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97730]) ).
fof(f97730,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f3400]) ).
fof(f3400,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,[],[f3309,f291]) ).
fof(f3309,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,[],[f323,f278]) ).
fof(f278,plain,
! [X2,X0,X1] : or(X2,and(not(X0),not(X1))) = not(and(not(X2),or(X0,X1))),
inference(superposition,[],[f222,f222]) ).
fof(f98795,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97732]) ).
fof(f97732,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28071]) ).
fof(f28071,plain,
( ! [X0,X1] : is_a_theorem(implies(or(not(equiv(X0,X0)),X1),X1))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f28052,f279]) ).
fof(f28052,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(not(equiv(X0,X0))),X1),X1))
| ~ spl1_3 ),
inference(resolution,[],[f27576,f1685]) ).
fof(f98794,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97733]) ).
fof(f97733,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28317]) ).
fof(f28317,plain,
( ! [X0,X1] : is_a_theorem(implies(or(not(strict_equiv(X0,X0)),X1),X1))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f28298,f279]) ).
fof(f28298,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(not(strict_equiv(X0,X0))),X1),X1))
| ~ spl1_3 ),
inference(resolution,[],[f28245,f1685]) ).
fof(f98793,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97734]) ).
fof(f97734,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f225]) ).
fof(f98792,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97739]) ).
fof(f97739,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f227]) ).
fof(f98791,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97742]) ).
fof(f97742,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8260]) ).
fof(f8260,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f8229,f223]) ).
fof(f8229,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,X1)),X0)),
inference(resolution,[],[f5928,f225]) ).
fof(f98790,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97743]) ).
fof(f97743,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8842]) ).
fof(f8842,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,X1)),implies(X1,X0))),
inference(superposition,[],[f8803,f223]) ).
fof(f8803,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,X1)),X1)),
inference(resolution,[],[f5929,f225]) ).
fof(f98789,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97744]) ).
fof(f97744,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8262]) ).
fof(f8262,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(not(X0),X1)),or(X0,X1))),
inference(superposition,[],[f8229,f460]) ).
fof(f460,plain,
! [X0,X1] : equiv(not(X0),X1) = and(or(X0,X1),implies(X1,not(X0))),
inference(superposition,[],[f223,f279]) ).
fof(f98788,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97745]) ).
fof(f97745,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8843]) ).
fof(f8843,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,not(X1))),or(X1,X0))),
inference(superposition,[],[f8803,f461]) ).
fof(f461,plain,
! [X0,X1] : equiv(X1,not(X0)) = and(implies(X1,not(X0)),or(X0,X1)),
inference(superposition,[],[f223,f279]) ).
fof(f98787,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97751]) ).
fof(f97751,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f625]) ).
fof(f625,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(not(X0)),implies(possibly(X0),X1))),
inference(superposition,[],[f230,f283]) ).
fof(f98786,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97752]) ).
fof(f97752,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6053]) ).
fof(f6053,plain,
! [X0] : is_a_theorem(implies(necessarily(not(X0)),not(necessarily(possibly(X0))))),
inference(resolution,[],[f5944,f332]) ).
fof(f332,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(f98785,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97753]) ).
fof(f97753,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18124]) ).
fof(f18124,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(X0)),not(possibly(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f18093,f221]) ).
fof(f98784,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97754]) ).
fof(f97754,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f332]) ).
fof(f98783,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97755]) ).
fof(f97755,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24791]) ).
fof(f24791,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f20953,f10246]) ).
fof(f10246,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f10232,f218]) ).
fof(f10232,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(equiv(X1,X1),X0))) ),
inference(resolution,[],[f9803,f1594]) ).
fof(f20953,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(necessarily(not(X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19285,f1842]) ).
fof(f98782,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97756]) ).
fof(f97756,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50951]) ).
fof(f50951,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(not(necessarily(X0)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f6400,f18240]) ).
fof(f18240,plain,
( ! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18137,f1842]) ).
fof(f6400,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,necessarily(X1)))
| is_a_theorem(implies(necessarily(X0),X1)) ),
inference(resolution,[],[f6051,f5944]) ).
fof(f6051,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f5944,f551]) ).
fof(f98781,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97757]) ).
fof(f97757,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f51022]) ).
fof(f51022,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(not(necessarily(necessarily(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f50951,f5944]) ).
fof(f98780,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97758]) ).
fof(f97758,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24797]) ).
fof(f24797,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(strict_equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f20953,f10269]) ).
fof(f10269,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(strict_equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f10255,f218]) ).
fof(f10255,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(strict_equiv(X1,X1),X0))) ),
inference(resolution,[],[f9815,f1594]) ).
fof(f98779,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97760]) ).
fof(f97760,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24799]) ).
fof(f24799,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(possibly(equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f20953,f14872]) ).
fof(f14872,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f14857,f218]) ).
fof(f14857,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(possibly(equiv(X1,X1)),X0))) ),
inference(resolution,[],[f11773,f1594]) ).
fof(f98778,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97761]) ).
fof(f97761,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24800]) ).
fof(f24800,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(possibly(strict_equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f20953,f14999]) ).
fof(f14999,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f14984,f218]) ).
fof(f14984,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(possibly(strict_equiv(X1,X1)),X0))) ),
inference(resolution,[],[f12155,f1594]) ).
fof(f98777,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97762]) ).
fof(f97762,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50949]) ).
fof(f50949,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(possibly(X0))),not(X0)))
| ~ spl1_3 ),
inference(resolution,[],[f6400,f18322]) ).
fof(f18322,plain,
( ! [X0] : is_a_theorem(strict_implies(not(possibly(X0)),necessarily(not(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f18240,f221]) ).
fof(f98776,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97763]) ).
fof(f97763,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8229]) ).
fof(f98775,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97764]) ).
fof(f97764,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8258]) ).
fof(f8258,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(X0),X1)),X0)),
inference(resolution,[],[f8229,f5944]) ).
fof(f98774,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97765]) ).
fof(f97765,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8341]) ).
fof(f8341,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(necessarily(X0)),X1)),X0)),
inference(resolution,[],[f8258,f5944]) ).
fof(f98773,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97766]) ).
fof(f97766,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50285]) ).
fof(f50285,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(necessarily(necessarily(X0))),X1)),X0)),
inference(resolution,[],[f6072,f8258]) ).
fof(f98772,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97767]) ).
fof(f97767,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f31716]) ).
fof(f31716,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(and(not(not(X0)),X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f22659,f1653]) ).
fof(f22659,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(necessarily(and(not(X0),X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f1842]) ).
fof(f98771,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97768]) ).
fof(f97768,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8255]) ).
fof(f8255,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,X1),X2)),X0)),
inference(resolution,[],[f8229,f5928]) ).
fof(f98770,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97769]) ).
fof(f97769,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8434]) ).
fof(f8434,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(necessarily(X0),X1),X2)),X0)),
inference(resolution,[],[f8255,f5944]) ).
fof(f98769,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97770]) ).
fof(f97770,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8338]) ).
fof(f8338,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(and(X0,X1)),X2)),X0)),
inference(resolution,[],[f8258,f5928]) ).
fof(f98768,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97771]) ).
fof(f97771,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8803]) ).
fof(f98767,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97772]) ).
fof(f97772,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f31537]) ).
fof(f31537,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,not(not(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f22640,f1653]) ).
fof(f22640,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(necessarily(and(X1,not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18396,f1842]) ).
fof(f98766,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97773]) ).
fof(f97773,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8837]) ).
fof(f8837,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,X2))),X1)),
inference(resolution,[],[f8803,f5928]) ).
fof(f98765,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97774]) ).
fof(f97774,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9139]) ).
fof(f9139,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(necessarily(X1),X2))),X1)),
inference(resolution,[],[f8837,f5944]) ).
fof(f98764,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97775]) ).
fof(f97775,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8840]) ).
fof(f8840,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(X1))),X1)),
inference(resolution,[],[f8803,f5944]) ).
fof(f98763,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97776]) ).
fof(f97776,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8967]) ).
fof(f8967,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(necessarily(X1)))),X1)),
inference(resolution,[],[f8840,f5944]) ).
fof(f98762,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97777]) ).
fof(f97777,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50292]) ).
fof(f50292,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6072,f8840]) ).
fof(f98761,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97778]) ).
fof(f97778,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8964]) ).
fof(f8964,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(and(X1,X2)))),X1)),
inference(resolution,[],[f8840,f5928]) ).
fof(f98760,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97779]) ).
fof(f97779,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8807]) ).
fof(f8807,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,X1),X2)),X1)),
inference(resolution,[],[f5929,f8229]) ).
fof(f98759,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97780]) ).
fof(f97780,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9095]) ).
fof(f9095,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,necessarily(X1)),X2)),X1)),
inference(resolution,[],[f8807,f5944]) ).
fof(f98758,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97781]) ).
fof(f97781,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8808]) ).
fof(f8808,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(and(X0,X1)),X2)),X1)),
inference(resolution,[],[f5929,f8258]) ).
fof(f98757,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97782]) ).
fof(f97782,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8836]) ).
fof(f8836,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,X2))),X2)),
inference(resolution,[],[f8803,f5929]) ).
fof(f98756,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97783]) ).
fof(f97783,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9121]) ).
fof(f9121,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,necessarily(X2)))),X2)),
inference(resolution,[],[f8836,f5944]) ).
fof(f98755,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97784]) ).
fof(f97784,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8963]) ).
fof(f8963,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(and(X1,X2)))),X2)),
inference(resolution,[],[f8840,f5929]) ).
fof(f98754,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97785]) ).
fof(f97785,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6052]) ).
fof(f98753,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97786]) ).
fof(f97786,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23594]) ).
fof(f23594,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(not(X0)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f1653]) ).
fof(f20186,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(necessarily(not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18398,f1842]) ).
fof(f98752,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97787]) ).
fof(f97787,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24970]) ).
fof(f24970,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(not(necessarily(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23594,f5944]) ).
fof(f98751,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97788]) ).
fof(f97788,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8233]) ).
fof(f8233,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,X1))),X0)),
inference(resolution,[],[f5928,f6052]) ).
fof(f98750,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97789]) ).
fof(f97789,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8324]) ).
fof(f8324,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(necessarily(X0),X1))),X0)),
inference(resolution,[],[f8233,f5944]) ).
fof(f98749,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97790]) ).
fof(f97790,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50299]) ).
fof(f50299,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(necessarily(necessarily(X0)),X1))),X0)),
inference(resolution,[],[f6072,f8233]) ).
fof(f98748,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97791]) ).
fof(f97791,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8321]) ).
fof(f8321,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(and(X0,X1),X2))),X0)),
inference(resolution,[],[f8233,f5928]) ).
fof(f98747,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97792]) ).
fof(f97792,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6079]) ).
fof(f6079,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(X0))),X0)),
inference(resolution,[],[f6052,f5944]) ).
fof(f98746,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97793]) ).
fof(f97793,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f38265]) ).
fof(f38265,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(not(not(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23699,f1653]) ).
fof(f23699,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(necessarily(necessarily(not(X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20191,f1842]) ).
fof(f98745,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97794]) ).
fof(f97794,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8234]) ).
fof(f8234,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,X1)))),X0)),
inference(resolution,[],[f5928,f6079]) ).
fof(f98744,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97795]) ).
fof(f97795,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8511]) ).
fof(f8511,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(necessarily(X0),X1)))),X0)),
inference(resolution,[],[f8234,f5944]) ).
fof(f98743,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97796]) ).
fof(f97796,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6138]) ).
fof(f6138,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(X0)))),X0)),
inference(resolution,[],[f6079,f5944]) ).
fof(f98742,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97797]) ).
fof(f97797,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6234]) ).
fof(f6234,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(necessarily(X0))))),X0)),
inference(resolution,[],[f6138,f5944]) ).
fof(f98741,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97798]) ).
fof(f97798,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8235]) ).
fof(f8235,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(and(X0,X1))))),X0)),
inference(resolution,[],[f5928,f6138]) ).
fof(f98740,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97801]) ).
fof(f97801,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28201]) ).
fof(f28201,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(not(equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18622,f20958]) ).
fof(f98739,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97802]) ).
fof(f97802,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28450]) ).
fof(f28450,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(not(strict_equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19124,f20958]) ).
fof(f98738,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97803]) ).
fof(f97803,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8811]) ).
fof(f8811,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,X1))),X1)),
inference(resolution,[],[f5929,f6052]) ).
fof(f98737,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97804]) ).
fof(f97804,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8949]) ).
fof(f8949,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,necessarily(X1)))),X1)),
inference(resolution,[],[f8811,f5944]) ).
fof(f98736,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97805]) ).
fof(f97805,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50310]) ).
fof(f50310,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6072,f8811]) ).
fof(f98735,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97806]) ).
fof(f97806,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8946]) ).
fof(f8946,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,and(X1,X2)))),X1)),
inference(resolution,[],[f8811,f5928]) ).
fof(f98734,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97807]) ).
fof(f97807,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8816]) ).
fof(f8816,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(and(X0,X1),X2))),X1)),
inference(resolution,[],[f5929,f8233]) ).
fof(f98733,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97808]) ).
fof(f97808,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8812]) ).
fof(f8812,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,X1)))),X1)),
inference(resolution,[],[f5929,f6079]) ).
fof(f98732,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97809]) ).
fof(f97809,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9219]) ).
fof(f9219,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,necessarily(X1))))),X1)),
inference(resolution,[],[f8812,f5944]) ).
fof(f98731,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97810]) ).
fof(f97810,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8813]) ).
fof(f8813,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(and(X0,X1))))),X1)),
inference(resolution,[],[f5929,f6138]) ).
fof(f98730,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97811]) ).
fof(f97811,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8945]) ).
fof(f8945,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,and(X1,X2)))),X2)),
inference(resolution,[],[f8811,f5929]) ).
fof(f98729,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97812]) ).
fof(f97812,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6139]) ).
fof(f6139,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(strict_implies(X0,X1))),implies(X0,X1))),
inference(superposition,[],[f6079,f218]) ).
fof(f98728,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97813]) ).
fof(f97813,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8326]) ).
fof(f8326,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(equiv(X0,X1))),implies(X0,X1))),
inference(superposition,[],[f8233,f223]) ).
fof(f98727,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97814]) ).
fof(f97814,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8951]) ).
fof(f8951,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(equiv(X0,X1))),implies(X1,X0))),
inference(superposition,[],[f8811,f223]) ).
fof(f98726,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97815]) ).
fof(f97815,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f42735]) ).
fof(f42735,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(possibly(X0)))),not(X0)))
| ~ spl1_3 ),
inference(superposition,[],[f24970,f221]) ).
fof(f98725,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97816]) ).
fof(f97816,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8325]) ).
fof(f8325,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(strict_equiv(X0,X1))),strict_implies(X0,X1))),
inference(superposition,[],[f8233,f220]) ).
fof(f98724,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97817]) ).
fof(f97817,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8950]) ).
fof(f8950,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(strict_equiv(X0,X1))),strict_implies(X1,X0))),
inference(superposition,[],[f8811,f220]) ).
fof(f98723,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97818]) ).
fof(f97818,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6080]) ).
fof(f6080,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_implies(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f6052,f218]) ).
fof(f98722,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97819]) ).
fof(f97819,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6081]) ).
fof(f6081,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_implies(not(X0),X1)),or(X0,X1))),
inference(superposition,[],[f6052,f291]) ).
fof(f98721,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97820]) ).
fof(f97820,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8259]) ).
fof(f8259,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_equiv(X0,X1)),strict_implies(X0,X1))),
inference(superposition,[],[f8229,f220]) ).
fof(f98720,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97821]) ).
fof(f97821,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f8841]) ).
fof(f8841,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_equiv(X0,X1)),strict_implies(X1,X0))),
inference(superposition,[],[f8803,f220]) ).
fof(f98719,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97823]) ).
fof(f97823,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f727]) ).
fof(f98718,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97824]) ).
fof(f97824,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f248]) ).
fof(f248,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f225,f218]) ).
fof(f98717,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97825]) ).
fof(f97825,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f505]) ).
fof(f98716,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97826]) ).
fof(f97826,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f407]) ).
fof(f407,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(f98715,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97827]) ).
fof(f97827,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f246]) ).
fof(f246,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),necessarily(strict_implies(X0,X1)))),
inference(superposition,[],[f227,f218]) ).
fof(f98714,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97830]) ).
fof(f97830,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f296]) ).
fof(f296,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f248,f279]) ).
fof(f98713,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97831]) ).
fof(f97831,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f552]) ).
fof(f552,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,X1),X2),implies(strict_implies(X0,X1),necessarily(X2)))),
inference(superposition,[],[f505,f218]) ).
fof(f98712,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97832]) ).
fof(f97832,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2185]) ).
fof(f2185,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),implies(strict_implies(not(X0),X1),necessarily(X2)))),
inference(superposition,[],[f552,f279]) ).
fof(f98711,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97833]) ).
fof(f97833,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2736]) ).
fof(f2736,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,[],[f552,f281]) ).
fof(f98710,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97834]) ).
fof(f97834,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f554]) ).
fof(f554,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,implies(X0,X1)),implies(necessarily(X2),strict_implies(X0,X1)))),
inference(superposition,[],[f505,f218]) ).
fof(f98709,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97835]) ).
fof(f97835,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2186]) ).
fof(f2186,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,[],[f552,f218]) ).
fof(f98708,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97836]) ).
fof(f97836,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2737]) ).
fof(f2737,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,[],[f554,f281]) ).
fof(f98707,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97837]) ).
fof(f97837,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2723]) ).
fof(f2723,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,f281]) ).
fof(f98706,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97838]) ).
fof(f97838,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2252]) ).
fof(f2252,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,or(X0,X1)),implies(necessarily(X2),strict_implies(not(X0),X1)))),
inference(superposition,[],[f554,f279]) ).
fof(f98705,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97839]) ).
fof(f97839,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f405]) ).
fof(f405,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X0,X1))),
inference(superposition,[],[f232,f220]) ).
fof(f98704,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97840]) ).
fof(f97840,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f406]) ).
fof(f406,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X1,X0))),
inference(superposition,[],[f233,f220]) ).
fof(f98703,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97841]) ).
fof(f97841,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50522]) ).
fof(f50522,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),implies(X0,X1))),
inference(superposition,[],[f6117,f220]) ).
fof(f98702,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97842]) ).
fof(f97842,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50767]) ).
fof(f50767,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),implies(X1,X0))),
inference(superposition,[],[f6128,f220]) ).
fof(f98701,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97843]) ).
fof(f97843,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50552]) ).
fof(f50552,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f50522,f279]) ).
fof(f98700,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97844]) ).
fof(f97844,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f50797]) ).
fof(f50797,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X1,not(X0)),or(X0,X1))),
inference(superposition,[],[f50767,f279]) ).
fof(f98699,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97846]) ).
fof(f97846,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f739]) ).
fof(f739,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(subsumption_resolution,[],[f737,f701]) ).
fof(f737,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[],[f726,f223]) ).
fof(f726,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f702,f242]) ).
fof(f98698,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97857]) ).
fof(f97857,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92645]) ).
fof(f92645,plain,
( ! [X0] : is_a_theorem(not(not(implies(X0,X0))))
| ~ spl1_3 ),
inference(resolution,[],[f92627,f18354]) ).
fof(f18354,plain,
( ! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(not(not(X0))) )
| ~ spl1_3 ),
inference(resolution,[],[f18287,f2156]) ).
fof(f2156,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f1836,f242]) ).
fof(f1836,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1147,f261]) ).
fof(f1147,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(or(X0,X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1146,f218]) ).
fof(f1146,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(implies(or(X0,X0),X1))) ),
inference(forward_demodulation,[],[f1106,f218]) ).
fof(f1106,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(or(X0,X0),X1))) ),
inference(resolution,[],[f919,f758]) ).
fof(f18287,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(not(X0))))
| ~ spl1_3 ),
inference(resolution,[],[f18238,f1842]) ).
fof(f92627,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[],[f92490,f279]) ).
fof(f98697,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97858]) ).
fof(f97858,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18115]) ).
fof(f18115,plain,
( ! [X0] : is_a_theorem(not(not(equiv(X0,X0))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f9818]) ).
fof(f98696,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97860]) ).
fof(f97860,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f27583]) ).
fof(f27583,plain,
( ! [X0] : is_a_theorem(not(not(not(not(equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18619,f18137]) ).
fof(f98695,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97861]) ).
fof(f97861,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28252]) ).
fof(f28252,plain,
( ! [X0] : is_a_theorem(not(not(not(not(strict_equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f19121,f18137]) ).
fof(f98694,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97866]) ).
fof(f97866,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f93869]) ).
fof(f93869,plain,
( ! [X0] : is_a_theorem(not(not(or(X0,not(X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f93788,f18354]) ).
fof(f93788,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X1)))),
inference(superposition,[],[f92492,f279]) ).
fof(f98693,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97871]) ).
fof(f97871,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f41532]) ).
fof(f98692,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97872]) ).
fof(f97872,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f41560]) ).
fof(f98691,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97873]) ).
fof(f97873,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18119]) ).
fof(f18119,plain,
( ! [X0] : is_a_theorem(not(not(strict_equiv(X0,X0))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f9835]) ).
fof(f98690,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97876]) ).
fof(f97876,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18122]) ).
fof(f18122,plain,
( ! [X0] : is_a_theorem(not(not(possibly(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f11748]) ).
fof(f98689,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97877]) ).
fof(f97877,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18123]) ).
fof(f18123,plain,
( ! [X0] : is_a_theorem(not(not(possibly(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f12130]) ).
fof(f98688,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97882]) ).
fof(f97882,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2703]) ).
fof(f2703,plain,
! [X0] : is_a_theorem(not(and(not(X0),or(X0,X0)))),
inference(superposition,[],[f702,f281]) ).
fof(f98687,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97883]) ).
fof(f97883,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2707]) ).
fof(f2707,plain,
! [X0,X1] : is_a_theorem(not(and(and(not(X0),not(X1)),or(X0,X1)))),
inference(superposition,[],[f701,f281]) ).
fof(f98686,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97884]) ).
fof(f97884,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2754]) ).
fof(f2754,plain,
! [X2,X0,X1] : is_a_theorem(not(and(and(and(not(X0),not(X1)),X2),or(X0,X1)))),
inference(superposition,[],[f232,f281]) ).
fof(f98685,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97885]) ).
fof(f97885,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2755]) ).
fof(f2755,plain,
! [X2,X0,X1] : is_a_theorem(not(and(and(X0,and(not(X1),not(X2))),or(X1,X2)))),
inference(superposition,[],[f233,f281]) ).
fof(f98684,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97886]) ).
fof(f97886,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2762]) ).
fof(f2762,plain,
! [X0,X1] : is_a_theorem(not(and(necessarily(and(not(X0),not(X1))),or(X0,X1)))),
inference(superposition,[],[f225,f281]) ).
fof(f98683,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97893]) ).
fof(f97893,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23104]) ).
fof(f23104,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f10246]) ).
fof(f98682,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97894]) ).
fof(f97894,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23112]) ).
fof(f23112,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(strict_equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f10269]) ).
fof(f98681,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97896]) ).
fof(f97896,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23171]) ).
fof(f23171,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(possibly(equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19254,f11748]) ).
fof(f98680,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97897]) ).
fof(f97897,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23172]) ).
fof(f23172,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(possibly(strict_equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19254,f12130]) ).
fof(f98679,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97900]) ).
fof(f97900,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28212]) ).
fof(f28212,plain,
( ! [X0,X1] : is_a_theorem(not(and(necessarily(not(equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f18622,f19258]) ).
fof(f98678,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97901]) ).
fof(f97901,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28462]) ).
fof(f28462,plain,
( ! [X0,X1] : is_a_theorem(not(and(necessarily(not(strict_equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19124,f19258]) ).
fof(f98677,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97904]) ).
fof(f97904,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28211]) ).
fof(f28211,plain,
( ! [X0,X1] : is_a_theorem(not(and(X0,necessarily(not(equiv(X1,X1))))))
| ~ spl1_3 ),
inference(resolution,[],[f18622,f19163]) ).
fof(f98676,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97905]) ).
fof(f97905,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28461]) ).
fof(f28461,plain,
( ! [X0,X1] : is_a_theorem(not(and(X0,necessarily(not(strict_equiv(X1,X1))))))
| ~ spl1_3 ),
inference(resolution,[],[f19124,f19163]) ).
fof(f98675,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97911]) ).
fof(f97911,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28216]) ).
fof(f28216,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18622,f18397]) ).
fof(f98674,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97912]) ).
fof(f97912,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28466]) ).
fof(f28466,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19124,f18397]) ).
fof(f98673,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97914]) ).
fof(f97914,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28217]) ).
fof(f28217,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(X0,not(equiv(X1,X1))))))
| ~ spl1_3 ),
inference(resolution,[],[f18622,f18396]) ).
fof(f98672,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97915]) ).
fof(f97915,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28467]) ).
fof(f28467,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(X0,not(strict_equiv(X1,X1))))))
| ~ spl1_3 ),
inference(resolution,[],[f19124,f18396]) ).
fof(f98671,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97920]) ).
fof(f97920,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23593]) ).
fof(f23593,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f10246]) ).
fof(f98670,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97921]) ).
fof(f97921,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23601]) ).
fof(f23601,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(strict_equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f10269]) ).
fof(f98669,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97923]) ).
fof(f97923,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23658]) ).
fof(f23658,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(possibly(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20187,f11748]) ).
fof(f98668,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97924]) ).
fof(f97924,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23659]) ).
fof(f23659,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(possibly(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20187,f12130]) ).
fof(f98667,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97927]) ).
fof(f97927,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28215]) ).
fof(f28215,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f18622,f20191]) ).
fof(f98666,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97928]) ).
fof(f97928,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28465]) ).
fof(f28465,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f19124,f20191]) ).
fof(f98665,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97936]) ).
fof(f97936,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f21928]) ).
fof(f21928,plain,
( ! [X0] : is_a_theorem(not(possibly(not(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18154,f18113]) ).
fof(f98664,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97937]) ).
fof(f97937,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f21929]) ).
fof(f21929,plain,
( ! [X0] : is_a_theorem(not(possibly(not(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18154,f18117]) ).
fof(f98663,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97939]) ).
fof(f97939,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f32252]) ).
fof(f98662,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97940]) ).
fof(f97940,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f32327]) ).
fof(f98661,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97942]) ).
fof(f97942,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f36027]) ).
fof(f36027,plain,
( ! [X0] : is_a_theorem(not(possibly(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f23592,f18154]) ).
fof(f23592,plain,
( ! [X0] : is_a_theorem(necessarily(not(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f10245]) ).
fof(f98660,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97943]) ).
fof(f97943,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f36048]) ).
fof(f36048,plain,
( ! [X0] : is_a_theorem(not(possibly(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f23600,f18154]) ).
fof(f23600,plain,
( ! [X0] : is_a_theorem(necessarily(not(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f10268]) ).
fof(f98659,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97963]) ).
fof(f97963,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9822]) ).
fof(f9822,plain,
! [X0] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f9804,f2659]) ).
fof(f2659,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(and(X0,X0)) ),
inference(resolution,[],[f2156,f2123]) ).
fof(f2123,plain,
! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(resolution,[],[f1828,f234]) ).
fof(f1828,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1139,f247]) ).
fof(f1139,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1138,f218]) ).
fof(f1138,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(forward_demodulation,[],[f1102,f218]) ).
fof(f1102,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,implies(X0,X1))))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f919,f238]) ).
fof(f98658,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97964]) ).
fof(f97964,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11201]) ).
fof(f11201,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),equiv(X1,X1))),
inference(resolution,[],[f10385,f9818]) ).
fof(f98657,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97965]) ).
fof(f97965,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11202]) ).
fof(f11202,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),strict_equiv(X1,X1))),
inference(resolution,[],[f10385,f9835]) ).
fof(f98656,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97967]) ).
fof(f97967,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12755]) ).
fof(f12755,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),possibly(equiv(X1,X1)))),
inference(resolution,[],[f11961,f9818]) ).
fof(f98655,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97968]) ).
fof(f97968,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12759]) ).
fof(f12759,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f11961,f9835]) ).
fof(f98654,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97977]) ).
fof(f97977,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11248]) ).
fof(f11248,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),equiv(X1,X1))),
inference(resolution,[],[f10689,f9818]) ).
fof(f98653,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97978]) ).
fof(f97978,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9839]) ).
fof(f9839,plain,
! [X0] : is_a_theorem(and(strict_equiv(X0,X0),strict_equiv(X0,X0))),
inference(resolution,[],[f9816,f2659]) ).
fof(f98652,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97979]) ).
fof(f97979,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11249]) ).
fof(f11249,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),strict_equiv(X1,X1))),
inference(resolution,[],[f10689,f9835]) ).
fof(f98651,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97981]) ).
fof(f97981,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12862]) ).
fof(f12862,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),possibly(equiv(X1,X1)))),
inference(resolution,[],[f12270,f9818]) ).
fof(f98650,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97982]) ).
fof(f97982,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12866]) ).
fof(f12866,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12270,f9835]) ).
fof(f98649,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97989]) ).
fof(f97989,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f15018]) ).
fof(f15018,plain,
! [X0,X1] : is_a_theorem(and(possibly(equiv(X0,X0)),equiv(X1,X1))),
inference(resolution,[],[f14430,f9818]) ).
fof(f98648,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97990]) ).
fof(f97990,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f15022]) ).
fof(f15022,plain,
! [X0,X1] : is_a_theorem(and(possibly(equiv(X0,X0)),strict_equiv(X1,X1))),
inference(resolution,[],[f14430,f9835]) ).
fof(f98647,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97992]) ).
fof(f97992,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f15062]) ).
fof(f15062,plain,
! [X0,X1] : is_a_theorem(and(possibly(strict_equiv(X0,X0)),equiv(X1,X1))),
inference(resolution,[],[f14883,f9818]) ).
fof(f98646,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97993]) ).
fof(f97993,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f15066]) ).
fof(f15066,plain,
! [X0,X1] : is_a_theorem(and(possibly(strict_equiv(X0,X0)),strict_equiv(X1,X1))),
inference(resolution,[],[f14883,f9835]) ).
fof(f98645,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97998]) ).
fof(f97998,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92627]) ).
fof(f98644,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98004]) ).
fof(f98004,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f298]) ).
fof(f98643,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98005]) ).
fof(f98005,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f299]) ).
fof(f299,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,and(not(X0),X1)))),
inference(superposition,[],[f234,f279]) ).
fof(f98642,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98007]) ).
fof(f98007,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20955]) ).
fof(f20955,plain,
( ! [X0,X1] : is_a_theorem(or(X0,implies(necessarily(not(not(X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19285,f855]) ).
fof(f98641,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98008]) ).
fof(f98008,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9804]) ).
fof(f98640,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98009]) ).
fof(f98009,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f716]) ).
fof(f98639,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98012]) ).
fof(f98012,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f27593]) ).
fof(f27593,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(not(equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f18619,f302]) ).
fof(f302,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[],[f229,f279]) ).
fof(f98638,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98013]) ).
fof(f98013,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18137]) ).
fof(f98637,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98014]) ).
fof(f98014,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28263]) ).
fof(f28263,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f19121,f302]) ).
fof(f98636,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98015]) ).
fof(f98015,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2771]) ).
fof(f98635,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98016]) ).
fof(f98016,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19255]) ).
fof(f19255,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(and(not(not(X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f855]) ).
fof(f98634,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98017]) ).
fof(f98017,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20188]) ).
fof(f20188,plain,
( ! [X0] : is_a_theorem(or(X0,not(necessarily(necessarily(not(not(X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f18398,f855]) ).
fof(f98633,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98023]) ).
fof(f98023,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10397]) ).
fof(f10397,plain,
! [X0,X1] : is_a_theorem(or(X0,and(equiv(X1,X1),not(X0)))),
inference(resolution,[],[f9818,f301]) ).
fof(f98632,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98024]) ).
fof(f98024,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f729]) ).
fof(f729,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f702,f279]) ).
fof(f98631,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98025]) ).
fof(f98025,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10701]) ).
fof(f10701,plain,
! [X0,X1] : is_a_theorem(or(X0,and(strict_equiv(X1,X1),not(X0)))),
inference(resolution,[],[f9835,f301]) ).
fof(f98630,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98027]) ).
fof(f98027,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f302]) ).
fof(f98629,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98028]) ).
fof(f98028,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f93788]) ).
fof(f98628,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98029]) ).
fof(f98029,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f400]) ).
fof(f400,plain,
! [X0,X1] : is_a_theorem(or(X1,or(X0,and(not(X1),not(X0))))),
inference(superposition,[],[f299,f279]) ).
fof(f98627,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98034]) ).
fof(f98034,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f303]) ).
fof(f303,plain,
! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1))),
inference(superposition,[],[f230,f279]) ).
fof(f98626,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98035]) ).
fof(f98035,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f304]) ).
fof(f304,plain,
! [X0] : is_a_theorem(or(X0,necessarily(possibly(not(X0))))),
inference(superposition,[],[f226,f279]) ).
fof(f98625,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98042]) ).
fof(f98042,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45618]) ).
fof(f45618,plain,
( ! [X2,X0,X1] : is_a_theorem(or(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41532,f20642]) ).
fof(f20642,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X1,X0)) )
| ~ spl1_3 ),
inference(resolution,[],[f19174,f2939]) ).
fof(f2939,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(X0) ),
inference(resolution,[],[f2922,f287]) ).
fof(f287,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(f19174,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f222]) ).
fof(f98624,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98043]) ).
fof(f98043,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45648]) ).
fof(f45648,plain,
( ! [X2,X0,X1] : is_a_theorem(or(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41560,f20642]) ).
fof(f98623,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98046]) ).
fof(f98046,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f9816]) ).
fof(f98622,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98050]) ).
fof(f98050,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11716]) ).
fof(f98621,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98051]) ).
fof(f98051,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f6071]) ).
fof(f6071,plain,
! [X0] : is_a_theorem(or(X0,possibly(not(X0)))),
inference(superposition,[],[f6035,f279]) ).
fof(f98620,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98052]) ).
fof(f98052,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12098]) ).
fof(f98619,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98053]) ).
fof(f98053,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92644]) ).
fof(f92644,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X0),X1)),
inference(resolution,[],[f92627,f17182]) ).
fof(f17182,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f8179,f711]) ).
fof(f711,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f710,f279]) ).
fof(f710,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f708,f279]) ).
fof(f708,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f354,f279]) ).
fof(f8179,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f8175,f279]) ).
fof(f8175,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5909,f279]) ).
fof(f5909,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f230]) ).
fof(f98618,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98054]) ).
fof(f98054,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19268]) ).
fof(f98617,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98059]) ).
fof(f98059,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19173]) ).
fof(f19173,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),not(X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f219]) ).
fof(f98616,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98060]) ).
fof(f98060,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18139]) ).
fof(f18139,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1))))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f18111,f279]) ).
fof(f18111,plain,
( ! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),and(X0,not(X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f1299]) ).
fof(f98615,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98061]) ).
fof(f98061,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19285]) ).
fof(f98614,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98062]) ).
fof(f98062,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20958]) ).
fof(f98613,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98063]) ).
fof(f98063,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24911]) ).
fof(f24911,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(necessarily(necessarily(X0))),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f20958,f6062]) ).
fof(f98612,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98064]) ).
fof(f98064,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19283]) ).
fof(f98611,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98065]) ).
fof(f98065,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19284]) ).
fof(f98610,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98066]) ).
fof(f98066,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23545]) ).
fof(f23545,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,necessarily(X1)),X2),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19283,f6062]) ).
fof(f98609,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98067]) ).
fof(f98067,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23565]) ).
fof(f23565,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(necessarily(X0),X1),X2),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f6062]) ).
fof(f98608,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98068]) ).
fof(f98068,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20956]) ).
fof(f20956,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(necessarily(and(X0,X1)),X2),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19285,f8827]) ).
fof(f98607,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98069]) ).
fof(f98069,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20957]) ).
fof(f20957,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(necessarily(and(X0,X1)),X2),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19285,f8246]) ).
fof(f98606,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98071]) ).
fof(f98071,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19176]) ).
fof(f19176,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,necessarily(not(X1))),possibly(X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f263]) ).
fof(f98605,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98072]) ).
fof(f98072,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10402]) ).
fof(f10402,plain,
! [X0,X1] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(resolution,[],[f9818,f230]) ).
fof(f98604,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98075]) ).
fof(f98075,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18238]) ).
fof(f98603,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98076]) ).
fof(f98076,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19166]) ).
fof(f19166,plain,
( ! [X0,X1] : is_a_theorem(or(not(equiv(X0,X1)),implies(X1,X0)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f223]) ).
fof(f98602,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98077]) ).
fof(f98077,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19261]) ).
fof(f19261,plain,
( ! [X0,X1] : is_a_theorem(or(not(equiv(X0,X1)),implies(X0,X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18291,f223]) ).
fof(f98601,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98079]) ).
fof(f98079,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f27599]) ).
fof(f27599,plain,
( ! [X0,X1] : is_a_theorem(or(not(not(equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18619,f303]) ).
fof(f98600,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98080]) ).
fof(f98080,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28269]) ).
fof(f28269,plain,
( ! [X0,X1] : is_a_theorem(or(not(not(strict_equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19121,f303]) ).
fof(f98599,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98081]) ).
fof(f98081,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18290]) ).
fof(f98598,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98082]) ).
fof(f98082,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18291]) ).
fof(f98597,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98083]) ).
fof(f98083,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19163]) ).
fof(f98596,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98084]) ).
fof(f98084,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23037]) ).
fof(f23037,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,necessarily(necessarily(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19163,f6062]) ).
fof(f98595,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98085]) ).
fof(f98085,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19161]) ).
fof(f19161,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(X0,and(X1,X2))),X2))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f8827]) ).
fof(f98594,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98086]) ).
fof(f98086,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19162]) ).
fof(f19162,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(X0,and(X1,X2))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f8246]) ).
fof(f98593,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98087]) ).
fof(f98087,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19258]) ).
fof(f98592,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98088]) ).
fof(f98088,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23220]) ).
fof(f23220,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(necessarily(necessarily(X0)),X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19258,f6062]) ).
fof(f98591,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98089]) ).
fof(f98089,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19256]) ).
fof(f19256,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(and(X0,X1),X2)),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f8827]) ).
fof(f98590,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98090]) ).
fof(f98090,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19257]) ).
fof(f19257,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(and(X0,X1),X2)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f8246]) ).
fof(f98589,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98091]) ).
fof(f98091,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18292]) ).
fof(f98588,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98092]) ).
fof(f98092,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18398]) ).
fof(f98587,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98093]) ).
fof(f98093,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20191]) ).
fof(f98586,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98094]) ).
fof(f98094,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23705]) ).
fof(f23705,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(necessarily(necessarily(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f20191,f6062]) ).
fof(f98585,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98095]) ).
fof(f98095,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20190]) ).
fof(f20190,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(necessarily(and(X0,X1)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18398,f8246]) ).
fof(f98584,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98096]) ).
fof(f98096,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18397]) ).
fof(f98583,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98097]) ).
fof(f98097,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f22665]) ).
fof(f22665,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(necessarily(X0),X1))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f6062]) ).
fof(f98582,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98098]) ).
fof(f98098,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18396]) ).
fof(f98581,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98099]) ).
fof(f98099,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f22646]) ).
fof(f22646,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,necessarily(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18396,f6062]) ).
fof(f98580,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98100]) ).
fof(f98100,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20189]) ).
fof(f20189,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(necessarily(and(X0,X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18398,f8827]) ).
fof(f98579,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98101]) ).
fof(f98101,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18400]) ).
fof(f18400,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_implies(X0,X1)),implies(X0,X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18292,f218]) ).
fof(f98578,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98102]) ).
fof(f98102,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19165]) ).
fof(f19165,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_equiv(X0,X1)),strict_implies(X1,X0)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f220]) ).
fof(f98577,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98103]) ).
fof(f98103,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19260]) ).
fof(f19260,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_equiv(X0,X1)),strict_implies(X0,X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18291,f220]) ).
fof(f98576,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98107]) ).
fof(f98107,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f720]) ).
fof(f720,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X0,X1))),
inference(superposition,[],[f716,f219]) ).
fof(f98575,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98108]) ).
fof(f98108,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2775]) ).
fof(f2775,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,[],[f2718,f279]) ).
fof(f2718,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,f281]) ).
fof(f98574,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98109]) ).
fof(f98109,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2773]) ).
fof(f2773,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,[],[f2715,f279]) ).
fof(f2715,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,f281]) ).
fof(f98573,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98114]) ).
fof(f98114,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2783]) ).
fof(f2783,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,[],[f2782,f279]) ).
fof(f2782,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,[],[f2781,f281]) ).
fof(f2781,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,[],[f2780,f281]) ).
fof(f2780,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,[],[f2721,f279]) ).
fof(f2721,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,f281]) ).
fof(f98572,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98117]) ).
fof(f98117,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19174]) ).
fof(f98571,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98118]) ).
fof(f98118,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19269]) ).
fof(f19269,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0)))
| ~ spl1_3 ),
inference(superposition,[],[f18291,f222]) ).
fof(f98570,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98119]) ).
fof(f98119,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19177]) ).
fof(f19177,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,necessarily(not(X1))),possibly(X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f276]) ).
fof(f98569,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98120]) ).
fof(f98120,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f93868]) ).
fof(f93868,plain,
! [X0,X1] : is_a_theorem(or(or(X0,not(X0)),X1)),
inference(resolution,[],[f93788,f17182]) ).
fof(f98568,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98121]) ).
fof(f98121,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f305]) ).
fof(f305,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),implies(X1,possibly(X0)))),
inference(superposition,[],[f298,f221]) ).
fof(f98567,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98122]) ).
fof(f98122,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f309]) ).
fof(f309,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),or(X1,possibly(X0)))),
inference(superposition,[],[f302,f221]) ).
fof(f98566,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98123]) ).
fof(f98123,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f312]) ).
fof(f312,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),or(possibly(X0),X1))),
inference(superposition,[],[f303,f221]) ).
fof(f98565,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98124]) ).
fof(f98124,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f315]) ).
fof(f315,plain,
! [X0] : is_a_theorem(or(necessarily(not(X0)),necessarily(possibly(possibly(X0))))),
inference(superposition,[],[f304,f221]) ).
fof(f98564,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98129]) ).
fof(f98129,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45612]) ).
fof(f45612,plain,
( ! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f41532,f343]) ).
fof(f343,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f337,f279]) ).
fof(f337,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f322,f250]) ).
fof(f250,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f242,f229]) ).
fof(f98563,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98130]) ).
fof(f98130,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45642]) ).
fof(f45642,plain,
( ! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f41560,f343]) ).
fof(f98562,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98133]) ).
fof(f98133,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10706]) ).
fof(f10706,plain,
! [X0,X1] : is_a_theorem(or(strict_equiv(X0,X0),X1)),
inference(resolution,[],[f9835,f230]) ).
fof(f98561,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98136]) ).
fof(f98136,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f14452]) ).
fof(f14452,plain,
! [X0,X1] : is_a_theorem(or(possibly(equiv(X0,X0)),X1)),
inference(resolution,[],[f11748,f230]) ).
fof(f98560,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98137]) ).
fof(f98137,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f14905]) ).
fof(f14905,plain,
! [X0,X1] : is_a_theorem(or(possibly(strict_equiv(X0,X0)),X1)),
inference(resolution,[],[f12130,f230]) ).
fof(f98559,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98138]) ).
fof(f98138,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18403]) ).
fof(f18403,plain,
( ! [X0] : is_a_theorem(or(possibly(X0),not(X0)))
| ~ spl1_3 ),
inference(superposition,[],[f18292,f221]) ).
fof(f98558,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98139]) ).
fof(f98139,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18140]) ).
fof(f18140,plain,
( ! [X0] : is_a_theorem(or(possibly(X0),necessarily(not(X0))))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f18120,f279]) ).
fof(f18120,plain,
( ! [X0] : is_a_theorem(implies(not(possibly(X0)),necessarily(not(X0))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f637]) ).
fof(f637,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(X1)))
| is_a_theorem(implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f322,f283]) ).
fof(f98557,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98141]) ).
fof(f98141,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f5855]) ).
fof(f5855,plain,
! [X0] : is_a_theorem(necessarily(equiv(X0,X0))),
inference(subsumption_resolution,[],[f5848,f701]) ).
fof(f5848,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(resolution,[],[f5791,f2127]) ).
fof(f2127,plain,
! [X0] : is_a_theorem(strict_implies(implies(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f1828,f240]) ).
fof(f98556,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98146]) ).
fof(f98146,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18113]) ).
fof(f98555,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98147]) ).
fof(f98147,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18117]) ).
fof(f98554,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98149]) ).
fof(f98149,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23103]) ).
fof(f98553,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98150]) ).
fof(f98150,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23111]) ).
fof(f98552,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98153]) ).
fof(f98153,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23592]) ).
fof(f98551,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98154]) ).
fof(f98154,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23600]) ).
fof(f98550,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98166]) ).
fof(f98166,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11671]) ).
fof(f11671,plain,
! [X0] : is_a_theorem(necessarily(and(equiv(X0,X0),equiv(X0,X0)))),
inference(resolution,[],[f10235,f702]) ).
fof(f98549,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98167]) ).
fof(f98167,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11674]) ).
fof(f11674,plain,
! [X0,X1] : is_a_theorem(necessarily(and(equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10235,f10385]) ).
fof(f98548,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98169]) ).
fof(f98169,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12059]) ).
fof(f12059,plain,
! [X0,X1] : is_a_theorem(necessarily(and(equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10258,f10385]) ).
fof(f98547,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98170]) ).
fof(f98170,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12056]) ).
fof(f12056,plain,
! [X0] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),strict_equiv(X0,X0)))),
inference(resolution,[],[f10258,f702]) ).
fof(f98546,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98171]) ).
fof(f98171,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12060]) ).
fof(f12060,plain,
! [X0,X1] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10258,f10689]) ).
fof(f98545,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98173]) ).
fof(f98173,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11675]) ).
fof(f11675,plain,
! [X0,X1] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10235,f10689]) ).
fof(f98544,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98180]) ).
fof(f98180,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11687]) ).
fof(f98543,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98181]) ).
fof(f98181,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12072]) ).
fof(f98542,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98184]) ).
fof(f98184,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f5869]) ).
fof(f5869,plain,
! [X0] : is_a_theorem(necessarily(strict_implies(X0,X0))),
inference(resolution,[],[f5856,f1130]) ).
fof(f1130,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X1,X0))) ),
inference(resolution,[],[f919,f406]) ).
fof(f5856,plain,
! [X0] : is_a_theorem(necessarily(strict_equiv(X0,X0))),
inference(subsumption_resolution,[],[f5853,f1888]) ).
fof(f5853,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(necessarily(strict_equiv(X0,X0))) ),
inference(resolution,[],[f5791,f2132]) ).
fof(f2132,plain,
! [X0] : is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(resolution,[],[f1828,f407]) ).
fof(f98541,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98186]) ).
fof(f98186,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45616]) ).
fof(f45616,plain,
( ! [X0,X1] : is_a_theorem(necessarily(strict_implies(not(equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f41532,f18319]) ).
fof(f18319,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(necessarily(X0)) )
| ~ spl1_3 ),
inference(resolution,[],[f18240,f5791]) ).
fof(f98540,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98187]) ).
fof(f98187,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45646]) ).
fof(f45646,plain,
( ! [X0,X1] : is_a_theorem(necessarily(strict_implies(not(strict_equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f41560,f18319]) ).
fof(f98539,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98188]) ).
fof(f98188,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f5856]) ).
fof(f98538,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98198]) ).
fof(f98198,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10403]) ).
fof(f10403,plain,
! [X0] : is_a_theorem(necessarily(possibly(equiv(X0,X0)))),
inference(resolution,[],[f9818,f226]) ).
fof(f98537,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98201]) ).
fof(f98201,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f27600]) ).
fof(f27600,plain,
( ! [X0] : is_a_theorem(necessarily(possibly(not(not(equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18619,f304]) ).
fof(f98536,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98202]) ).
fof(f98202,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28270]) ).
fof(f28270,plain,
( ! [X0] : is_a_theorem(necessarily(possibly(not(not(strict_equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f19121,f304]) ).
fof(f98535,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98211]) ).
fof(f98211,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10707]) ).
fof(f10707,plain,
! [X0] : is_a_theorem(necessarily(possibly(strict_equiv(X0,X0)))),
inference(resolution,[],[f9835,f226]) ).
fof(f98534,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98214]) ).
fof(f98214,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f14453]) ).
fof(f14453,plain,
! [X0] : is_a_theorem(necessarily(possibly(possibly(equiv(X0,X0))))),
inference(resolution,[],[f11748,f226]) ).
fof(f98533,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98215]) ).
fof(f98215,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f14906]) ).
fof(f14906,plain,
! [X0] : is_a_theorem(necessarily(possibly(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f12130,f226]) ).
fof(f98532,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98216]) ).
fof(f98216,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f1888]) ).
fof(f98531,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98217]) ).
fof(f98217,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18240]) ).
fof(f98530,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98218]) ).
fof(f98218,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23106]) ).
fof(f23106,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f1155]) ).
fof(f98529,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98219]) ).
fof(f98219,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f32573]) ).
fof(f32573,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(necessarily(not(not(X0))),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23214,f1155]) ).
fof(f98528,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98220]) ).
fof(f98220,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23595]) ).
fof(f23595,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(necessarily(not(not(X0)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f1155]) ).
fof(f98527,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98221]) ).
fof(f98221,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f38266]) ).
fof(f38266,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(necessarily(necessarily(not(not(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23699,f1155]) ).
fof(f98526,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98222]) ).
fof(f98222,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f31717]) ).
fof(f31717,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(and(not(not(X0)),X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f22659,f1155]) ).
fof(f98525,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98232]) ).
fof(f98232,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11712]) ).
fof(f11712,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(equiv(X0,X0)),X1)),
inference(forward_demodulation,[],[f11686,f291]) ).
fof(f11686,plain,
! [X0,X1] : is_a_theorem(necessarily(or(equiv(X0,X0),X1))),
inference(resolution,[],[f10235,f230]) ).
fof(f98524,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98233]) ).
fof(f98233,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12094]) ).
fof(f12094,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(strict_equiv(X0,X0)),X1)),
inference(forward_demodulation,[],[f12071,f291]) ).
fof(f12071,plain,
! [X0,X1] : is_a_theorem(necessarily(or(strict_equiv(X0,X0),X1))),
inference(resolution,[],[f10258,f230]) ).
fof(f98523,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98234]) ).
fof(f98234,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2885]) ).
fof(f2885,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(not(X0),or(X1,X0)),X1)),
inference(resolution,[],[f2771,f1842]) ).
fof(f98522,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98235]) ).
fof(f98235,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f31853]) ).
fof(f31853,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,necessarily(not(not(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f23031,f1155]) ).
fof(f98521,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98245]) ).
fof(f98245,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24822]) ).
fof(f24822,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f24790,f218]) ).
fof(f24790,plain,
( ! [X0,X1] : is_a_theorem(necessarily(implies(necessarily(not(equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20953,f10245]) ).
fof(f98520,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98246]) ).
fof(f98246,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24823]) ).
fof(f24823,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(strict_equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f24796,f218]) ).
fof(f24796,plain,
( ! [X0,X1] : is_a_theorem(necessarily(implies(necessarily(not(strict_equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20953,f10268]) ).
fof(f98519,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98248]) ).
fof(f98248,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f42076]) ).
fof(f42076,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(possibly(equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f24799,f1828]) ).
fof(f98518,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98249]) ).
fof(f98249,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f42101]) ).
fof(f42101,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(possibly(strict_equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f24800,f1828]) ).
fof(f98517,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98250]) ).
fof(f98250,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f31538]) ).
fof(f31538,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(and(X0,not(not(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f22640,f1155]) ).
fof(f98516,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98252]) ).
fof(f98252,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f36023]) ).
fof(f36023,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(necessarily(not(equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f23592,f1845]) ).
fof(f98515,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98253]) ).
fof(f98253,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f36044]) ).
fof(f36044,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(necessarily(not(strict_equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f23600,f1845]) ).
fof(f98514,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98258]) ).
fof(f98258,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f32248]) ).
fof(f32248,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f23103,f1845]) ).
fof(f98513,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98259]) ).
fof(f98259,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f32323]) ).
fof(f32323,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f23111,f1845]) ).
fof(f98512,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98263]) ).
fof(f98263,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f35078]) ).
fof(f35078,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X0,not(equiv(X1,X1))),X2))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f35044,f218]) ).
fof(f35044,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(implies(and(X0,not(equiv(X1,X1))),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f23539,f10245]) ).
fof(f23539,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,implies(and(X1,not(X0)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f19283,f1842]) ).
fof(f98511,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98264]) ).
fof(f98264,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f35079]) ).
fof(f35079,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X0,not(strict_equiv(X1,X1))),X2))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f35050,f218]) ).
fof(f35050,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(implies(and(X0,not(strict_equiv(X1,X1))),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f23539,f10268]) ).
fof(f98510,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98265]) ).
fof(f98265,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2129]) ).
fof(f2129,plain,
! [X0,X1] : is_a_theorem(strict_implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(resolution,[],[f1828,f244]) ).
fof(f98509,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98266]) ).
fof(f98266,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19181]) ).
fof(f19181,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X0)))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f19158,f219]) ).
fof(f19158,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(X1,not(X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f1842]) ).
fof(f98508,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98267]) ).
fof(f98267,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92728]) ).
fof(f92728,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X1))),
inference(resolution,[],[f92644,f1842]) ).
fof(f98507,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98273]) ).
fof(f98273,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20953]) ).
fof(f98506,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98274]) ).
fof(f98274,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24905]) ).
fof(f24905,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(necessarily(necessarily(not(X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20958,f1842]) ).
fof(f98505,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98275]) ).
fof(f98275,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23539]) ).
fof(f98504,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98276]) ).
fof(f98276,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23559]) ).
fof(f23559,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,implies(and(not(X0),X1),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f1842]) ).
fof(f98503,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98277]) ).
fof(f98277,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19317]) ).
fof(f19317,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(X0)),implies(possibly(X0),X1)))
| ~ spl1_3 ),
inference(superposition,[],[f19293,f283]) ).
fof(f19293,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,or(X0,X1)))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f19280,f279]) ).
fof(f19280,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(not(X0),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19268,f1842]) ).
fof(f98502,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98278]) ).
fof(f98278,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2127]) ).
fof(f98501,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98279]) ).
fof(f98279,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10652]) ).
fof(f10652,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,equiv(X1,X1))),
inference(resolution,[],[f10402,f1842]) ).
fof(f98500,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98281]) ).
fof(f98281,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18287]) ).
fof(f98499,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98283]) ).
fof(f98283,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28077]) ).
fof(f28077,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(not(equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f27583,f1881]) ).
fof(f1881,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f1861,f1155]) ).
fof(f98498,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98284]) ).
fof(f98284,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f28323]) ).
fof(f28323,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f28252,f1881]) ).
fof(f98497,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98285]) ).
fof(f98285,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19253]) ).
fof(f98496,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98286]) ).
fof(f98286,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23031]) ).
fof(f98495,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98287]) ).
fof(f98287,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23214]) ).
fof(f98494,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98288]) ).
fof(f98288,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f20186]) ).
fof(f98493,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98289]) ).
fof(f98289,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23699]) ).
fof(f98492,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98290]) ).
fof(f98290,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f22640]) ).
fof(f98491,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98291]) ).
fof(f98291,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f22659]) ).
fof(f98490,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98292]) ).
fof(f98292,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18372]) ).
fof(f18372,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(not(X0)),not(possibly(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f18287,f221]) ).
fof(f98489,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98293]) ).
fof(f98293,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18434]) ).
fof(f18434,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(not(X0)),not(necessarily(possibly(X0)))))
| ~ spl1_3 ),
inference(superposition,[],[f18408,f245]) ).
fof(f18408,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f18393,f221]) ).
fof(f18393,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(not(X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18292,f1842]) ).
fof(f98488,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98294]) ).
fof(f98294,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2123]) ).
fof(f98487,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98297]) ).
fof(f98297,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11703]) ).
fof(f11703,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,and(equiv(X1,X1),X0))),
inference(forward_demodulation,[],[f11666,f218]) ).
fof(f11666,plain,
! [X0,X1] : is_a_theorem(necessarily(implies(X0,and(equiv(X1,X1),X0)))),
inference(resolution,[],[f10235,f234]) ).
fof(f98486,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98298]) ).
fof(f98298,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12085]) ).
fof(f12085,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,and(strict_equiv(X1,X1),X0))),
inference(forward_demodulation,[],[f12051,f218]) ).
fof(f12051,plain,
! [X0,X1] : is_a_theorem(necessarily(implies(X0,and(strict_equiv(X1,X1),X0)))),
inference(resolution,[],[f10258,f234]) ).
fof(f98485,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98305]) ).
fof(f98305,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19208]) ).
fof(f19208,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X1,or(X0,X1)))
| ~ spl1_3 ),
inference(superposition,[],[f19181,f279]) ).
fof(f98484,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98306]) ).
fof(f98306,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f95561]) ).
fof(f95561,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,or(X1,not(X1)))),
inference(resolution,[],[f93868,f1842]) ).
fof(f98483,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98307]) ).
fof(f98307,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f19293]) ).
fof(f98482,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98312]) ).
fof(f98312,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18322]) ).
fof(f98481,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98315]) ).
fof(f98315,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45613]) ).
fof(f45613,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41532,f1881]) ).
fof(f98480,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98316]) ).
fof(f98316,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45643]) ).
fof(f45643,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41560,f1881]) ).
fof(f98479,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98319]) ).
fof(f98319,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2132]) ).
fof(f98478,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98320]) ).
fof(f98320,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f10730]) ).
fof(f10730,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,strict_equiv(X1,X1))),
inference(resolution,[],[f10706,f1842]) ).
fof(f98477,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98321]) ).
fof(f98321,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18408]) ).
fof(f98476,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98324]) ).
fof(f98324,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f14482]) ).
fof(f14482,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f14452,f1842]) ).
fof(f98475,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98325]) ).
fof(f98325,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f14935]) ).
fof(f14935,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f14905,f1842]) ).
fof(f98474,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98326]) ).
fof(f98326,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f2662]) ).
fof(f2662,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,f224,f227,f241,f218,f234,f235,f236,f242,f258,f249,f219,f262,f250,f251,f252,f256,f257,f247,f268,f269,f270,f271,f222,f278,f280,f281,f282,f248,f286,f253,f254,f255,f279,f288,f289,f290,f298,f306,f307,f308,f302,f310,f311,f303,f313,f314,f304,f316,f317,f261,f287,f318,f325,f245,f334,f329,f246,f322,f338,f339,f340,f337,f342,f341,f238,f358,f343,f368,f369,f370,f291,f377,f293,f379,f380,f381,f294,f383,f384,f385,f295,f296,f392,f393,f394,f395,f299,f397,f398,f399,f300,f402,f403,f404,f220,f408,f411,f405,f412,f406,f413,f409,f410,f301,f415,f416,f417,f418,f305,f427,f428,f424,f309,f437,f438,f312,f447,f448,f315,f457,f458,f223,f460,f461,f464,f465,f468,f330,f374,f485,f486,f487,f376,f491,f492,f493,f378,f495,f496,f497,f382,f498,f499,f500,f505,f553,f555,f240,f576,f577,f266,f580,f581,f582,f583,f584,f283,f637,f638,f625,f664,f627,f683,f693,f243,f699,f697,f700,f354,f706,f713,f701,f716,f721,f702,f728,f726,f739,f705,f757,f244,f760,f761,f762,f763,f727,f765,f729,f768,f769,f736,f720,f786,f787,f788,f789,f551,f793,f794,f795,f796,f263,f801,f843,f803,f804,f844,f806,f807,f845,f809,f810,f811,f812,f813,f814,f815,f816,f817,f818,f846,f847,f848,f849,f823,f824,f825,f829,f830,f831,f832,f852,f836,f837,f838,f326,f857,f858,f859,f860,f331,f332,f892,f357,f899,f711,f758,f917,f918,f792,f920,f400,f924,f925,f926,f928,f929,f930,f323,f938,f941,f954,f585,f855,f995,f996,f997,f998,f916,f1002,f1003,f276,f1064,f1065,f1007,f1066,f1014,f1072,f1016,f1073,f1074,f1019,f1020,f1075,f1022,f1023,f1024,f1025,f1026,f1027,f1028,f1029,f1030,f1031,f1076,f1077,f1078,f1079,f1036,f1037,f1080,f1039,f1081,f1041,f1045,f1046,f1047,f1048,f1049,f1050,f1084,f1054,f1055,f1056,f1058,f919,f1135,f1136,f1141,f1143,f1145,f1151,f1152,f1153,f1157,f1159,f1161,f1121,f1123,f1164,f1132,f1133,f1166,f1169,f1178,f1170,f1097,f1187,f1189,f1186,f1101,f1204,f1205,f1201,f1203,f1211,f1212,f1210,f1217,f1218,f1112,f1234,f1236,f1233,f1113,f1245,f1247,f1244,f1137,f1264,f1259,f1260,f1261,f1262,f1263,f1254,f284,f1271,f1272,f1273,f1274,f1275,f1277,f1278,f1281,f1282,f1284,f1296,f1299,f1300,f1303,f1304,f1315,f1181,f1341,f1343,f1348,f1349,f1350,f1351,f1242,f1368,f1367,f1253,f1374,f1373,f1134,f1414,f1418,f1420,f407,f1425,f1424,f1148,f1149,f1150,f1416,f1432,f1435,f1438,f1437,f1182,f1443,f1444,f1198,f1240,f1251,f1434,f1466,f1468,f575,f1572,f1570,f1571,f1001,f1595,f1598,f1599,f1594,f1606,f1610,f1646,f1647,f1648,f1649,f1650,f1651,f1622,f1623,f1652,f1653,f1654,f1655,f1656,f1633,f1634,f1635,f1637,f1638,f1640,f1645,f1631,f1659,f1660,f1624,f1663,f1664,f1625,f1667,f1668,f1607,f1680,f1682,f1620,f695,f1685,f1692,f1694,f1689,f1690,f1695,f1621,f1636,f1698,f1699,f1642,f1643,f264,f1705,f1706,f1710,f1777,f1712,f1713,f1778,f1715,f1716,f1717,f1779,f1719,f1720,f1721,f1722,f1723,f1724,f1725,f1726,f1727,f1728,f1729,f1780,f1781,f1782,f1783,f1734,f1735,f1784,f1737,f1785,f1739,f1745,f1746,f1747,f1748,f1749,f1750,f1788,f1754,f1755,f1756,f1758,f1763,f1792,f1765,f1096,f1814,f1816,f1128,f1129,f1130,f1139,f1825,f1826,f1833,f1831,f1147,f1840,f1837,f1838,f1839,f1155,f1843,f1844,f1859,f1847,f1848,f1849,f1850,f1851,f1852,f1853,f1854,f1855,f1856,f1857,f1858,f1845,f1868,f1869,f1870,f1871,f1872,f1861,f1881,f1882,f1883,f1884,f1885,f1886,f1887,f1842,f1893,f1894,f1895,f1896,f1897,f1898,f1899,f1900,f285,f1904,f1963,f1906,f1907,f1908,f1909,f1910,f1911,f1912,f1916,f1917,f1918,f1919,f1922,f1923,f1925,f1937,f1940,f1941,f1942,f1945,f1946,f1957,f1888,f1891,f1162,f2039,f2040,f2041,f2027,f2049,f2051,f324,f2069,f2071,f2058,f2059,f2060,f2061,f2062,f2063,f2064,f2065,f2066,f2067,f2068,f1417,f2076,f2077,f2078,f1828,f2130,f2131,f2137,f2138,f2123,f2143,f2144,f2127,f2148,f2132,f1836,f2162,f2163,f2157,f2158,f2159,f2160,f2161,f552,f2181,f2188,f2184,f2185,f2186,f2187,f554,f2248,f2255,f2251,f2252,f2253,f2254,f1270,f2368,f2369,f2370,f1860,f2381,f2385,f2387,f277,f2391,f2487,f2393,f2488,f2395,f2400,f2489,f2402,f2490,f2491,f2405,f2492,f2407,f2493,f2409,f2410,f2494,f2412,f2413,f2414,f2415,f2416,f2417,f2418,f2419,f2420,f2421,f2495,f2496,f2497,f2498,f2426,f2427,f2499,f2429,f2430,f2500,f2432,f2438,f2439,f2440,f2441,f2442,f2443,f2503,f2450,f2451,f2452,f2455,f2460,f2461,f2462,f2511,f2512,f2465,f2522,f2475,f2478,f2531,f2480,f1862,f2535,f2549,f2550,f2551,f2552,f2129,f2637,f2638,f2639,f2640,f2156,f2643,f2646,f2647,f2650,f2651,f2652,f2653,f2661,f2655,f2656,f2658,f2659,f2660]) ).
fof(f2660,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(or(strict_implies(X0,X0),strict_implies(X0,X0))) ),
inference(resolution,[],[f2156,f2132]) ).
fof(f2658,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(or(X1,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f2156,f1134]) ).
fof(f2656,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(or(implies(X0,X1),implies(X0,X1))) ),
inference(resolution,[],[f2156,f2129]) ).
fof(f2655,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(possibly(X1),possibly(X1)))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(resolution,[],[f2156,f2027]) ).
fof(f2661,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,[],[f2654,f283]) ).
fof(f2654,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,[],[f2156,f1862]) ).
fof(f2653,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,[],[f2156,f1860]) ).
fof(f2652,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,[],[f2156,f1147]) ).
fof(f2651,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(not(X1),not(X1)))
| ~ is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f2156,f376]) ).
fof(f2650,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(not(X1),not(X1)))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f2156,f1137]) ).
fof(f2647,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(equiv(X1,X0)) ),
inference(resolution,[],[f2156,f1242]) ).
fof(f2646,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f2156,f1253]) ).
fof(f2643,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f2156,f1888]) ).
fof(f2640,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,[],[f2129,f285]) ).
fof(f2639,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,[],[f2129,f284]) ).
fof(f2638,plain,
! [X0,X1] : is_a_theorem(strict_implies(implies(necessarily(not(X0)),X1),implies(implies(possibly(X0),necessarily(not(X0))),X1))),
inference(superposition,[],[f2129,f283]) ).
fof(f2637,plain,
! [X0,X1] : is_a_theorem(strict_implies(or(X0,X1),implies(or(not(X0),not(X0)),X1))),
inference(superposition,[],[f2129,f279]) ).
fof(f2552,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,[],[f2543,f291]) ).
fof(f2543,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,[],[f1862,f277]) ).
fof(f2551,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,[],[f2542,f218]) ).
fof(f2542,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,[],[f1862,f264]) ).
fof(f2550,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,[],[f2541,f291]) ).
fof(f2541,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,[],[f1862,f276]) ).
fof(f2549,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,[],[f2540,f218]) ).
fof(f2540,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,[],[f1862,f263]) ).
fof(f2535,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(resolution,[],[f1862,f261]) ).
fof(f1862,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(possibly(X0))) ),
inference(superposition,[],[f1845,f221]) ).
fof(f2480,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,[],[f1881,f277]) ).
fof(f2531,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,[],[f2479,f291]) ).
fof(f2479,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,[],[f1845,f277]) ).
fof(f2478,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,[],[f1842,f277]) ).
fof(f2475,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,[],[f1417,f277]) ).
fof(f2522,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,[],[f2472,f291]) ).
fof(f2472,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,[],[f1270,f277]) ).
fof(f2465,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,[],[f1182,f277]) ).
fof(f2512,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,[],[f2464,f291]) ).
fof(f2464,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,[],[f1181,f277]) ).
fof(f2511,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,[],[f2463,f291]) ).
fof(f2463,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,[],[f1162,f277]) ).
fof(f2462,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,[],[f1155,f277]) ).
fof(f2461,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,[],[f1155,f277]) ).
fof(f2460,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,[],[f1137,f277]) ).
fof(f2455,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,[],[f855,f277]) ).
fof(f2452,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,[],[f729,f277]) ).
fof(f2451,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,[],[f720,f277]) ).
fof(f2450,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),or(X0,and(X1,not(X2))))),
inference(superposition,[],[f716,f277]) ).
fof(f2503,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,[],[f2449,f291]) ).
fof(f2449,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,[],[f625,f277]) ).
fof(f2443,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,[],[f400,f277]) ).
fof(f2442,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,[],[f400,f277]) ).
fof(f2441,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,[],[f382,f277]) ).
fof(f2440,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,[],[f378,f277]) ).
fof(f2439,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,[],[f376,f277]) ).
fof(f2438,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,[],[f374,f277]) ).
fof(f2432,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,[],[f343,f277]) ).
fof(f2500,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,[],[f2431,f291]) ).
fof(f2431,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,[],[f332,f277]) ).
fof(f2430,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,[],[f326,f277]) ).
fof(f2499,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,[],[f2428,f291]) ).
fof(f2428,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,[],[f323,f277]) ).
fof(f2427,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,[],[f322,f277]) ).
fof(f2498,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,[],[f2425,f291]) ).
fof(f2425,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,[],[f315,f277]) ).
fof(f2497,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,[],[f2424,f291]) ).
fof(f2424,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,[],[f312,f277]) ).
fof(f2496,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,[],[f2423,f291]) ).
fof(f2423,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,[],[f309,f277]) ).
fof(f2495,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,[],[f2422,f291]) ).
fof(f2422,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,[],[f305,f277]) ).
fof(f2421,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),necessarily(possibly(or(X0,and(X1,not(X2))))))),
inference(superposition,[],[f304,f277]) ).
fof(f2420,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,[],[f303,f277]) ).
fof(f2419,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,[],[f302,f277]) ).
fof(f2418,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,[],[f301,f277]) ).
fof(f2417,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,[],[f300,f277]) ).
fof(f2416,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,[],[f299,f277]) ).
fof(f2415,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,[],[f298,f277]) ).
fof(f2414,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,[],[f296,f277]) ).
fof(f2413,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,[],[f294,f277]) ).
fof(f2412,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,[],[f293,f277]) ).
fof(f2494,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,[],[f2411,f284]) ).
fof(f2411,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,[],[f285,f277]) ).
fof(f2410,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,[],[f285,f277]) ).
fof(f2409,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,[],[f284,f277]) ).
fof(f2493,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,[],[f2408,f291]) ).
fof(f2408,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,[],[f283,f277]) ).
fof(f2407,plain,
! [X2,X3,X0,X1] : implies(or(X0,and(X1,not(X2))),X3) = or(and(not(X0),implies(X1,X2)),X3),
inference(superposition,[],[f279,f277]) ).
fof(f2492,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,[],[f2406,f263]) ).
fof(f2406,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,[],[f276,f277]) ).
fof(f2405,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,f277]) ).
fof(f2491,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,[],[f2404,f291]) ).
fof(f2404,plain,
! [X2,X0,X1] : not(necessarily(possibly(and(not(X0),implies(X1,X2))))) = possibly(necessarily(or(X0,and(X1,not(X2))))),
inference(superposition,[],[f245,f277]) ).
fof(f2490,plain,
! [X2,X3,X0,X1] : implies(or(X0,and(X1,not(X2))),X3) = or(and(not(X0),implies(X1,X2)),X3),
inference(forward_demodulation,[],[f2403,f219]) ).
fof(f2403,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,f277]) ).
fof(f2402,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,f277]) ).
fof(f2489,plain,
! [X2,X0,X1] : possibly(and(not(X0),implies(X1,X2))) = not(strict_implies(not(X0),and(X1,not(X2)))),
inference(forward_demodulation,[],[f2401,f291]) ).
fof(f2401,plain,
! [X2,X0,X1] : possibly(and(not(X0),implies(X1,X2))) = not(necessarily(or(X0,and(X1,not(X2))))),
inference(superposition,[],[f221,f277]) ).
fof(f2400,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,f277]) ).
fof(f2395,plain,
! [X2,X0,X1] : or(X2,and(not(X0),not(X1))) = not(and(not(X2),or(X0,X1))),
inference(superposition,[],[f277,f279]) ).
fof(f2488,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,[],[f2394,f264]) ).
fof(f2394,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,[],[f277,f277]) ).
fof(f2393,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,[],[f277,f264]) ).
fof(f2487,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,[],[f2392,f264]) ).
fof(f2392,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,[],[f277,f276]) ).
fof(f2391,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,[],[f277,f263]) ).
fof(f2387,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,[],[f2386,f218]) ).
fof(f2386,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,[],[f2384,f219]) ).
fof(f2384,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,[],[f1860,f266]) ).
fof(f2385,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(necessarily(possibly(X0)))),X1)) ),
inference(forward_demodulation,[],[f2383,f221]) ).
fof(f2383,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(necessarily(possibly(X0)))),X1))
| ~ is_a_theorem(necessarily(not(necessarily(not(X0))))) ),
inference(superposition,[],[f1860,f245]) ).
fof(f2381,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(implies(necessarily(possibly(X0)),X1)) ),
inference(resolution,[],[f1860,f261]) ).
fof(f1860,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(possibly(X0)),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1845,f331]) ).
fof(f2370,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,[],[f2359,f218]) ).
fof(f2359,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,[],[f1270,f264]) ).
fof(f2369,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,[],[f2358,f291]) ).
fof(f2358,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,[],[f1270,f276]) ).
fof(f2368,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,[],[f2357,f218]) ).
fof(f2357,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,[],[f1270,f263]) ).
fof(f1270,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(implies(possibly(X0),X1)) ),
inference(superposition,[],[f1254,f283]) ).
fof(f2254,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,[],[f554,f291]) ).
fof(f2253,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,[],[f554,f218]) ).
fof(f2251,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,[],[f554,f242]) ).
fof(f2255,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,[],[f2249,f218]) ).
fof(f2249,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,[],[f554,f919]) ).
fof(f2248,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,[],[f554,f1594]) ).
fof(f2187,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,[],[f552,f291]) ).
fof(f2184,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,[],[f552,f242]) ).
fof(f2188,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,[],[f2182,f218]) ).
fof(f2182,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,[],[f552,f919]) ).
fof(f2181,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,[],[f552,f1594]) ).
fof(f2161,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,[],[f1836,f285]) ).
fof(f2160,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,[],[f1836,f284]) ).
fof(f2159,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,[],[f1836,f283]) ).
fof(f2158,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(or(X0,X0),X1)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(resolution,[],[f1836,f354]) ).
fof(f2157,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,[],[f1836,f1828]) ).
fof(f2163,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,[],[f2154,f291]) ).
fof(f2154,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(or(X0,X0)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1836,f919]) ).
fof(f2162,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,[],[f2153,f291]) ).
fof(f2153,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(necessarily(or(X0,X0))) ),
inference(resolution,[],[f1836,f1594]) ).
fof(f2148,plain,
! [X0] : is_a_theorem(strict_implies(or(X0,not(X0)),equiv(not(X0),not(X0)))),
inference(superposition,[],[f2127,f279]) ).
fof(f2144,plain,
! [X0] : is_a_theorem(strict_implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f2123,f223]) ).
fof(f2143,plain,
! [X0] : is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(superposition,[],[f2123,f220]) ).
fof(f2138,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f2135,f279]) ).
fof(f2135,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,implies(not(X0),X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1828,f279]) ).
fof(f2137,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f2134,f279]) ).
fof(f2134,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1828,f279]) ).
fof(f2131,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,implies(or(X0,X0),X1))) ),
inference(resolution,[],[f1828,f916]) ).
fof(f2130,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[],[f1828,f695]) ).
fof(f2078,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,[],[f1417,f264]) ).
fof(f2077,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,[],[f1417,f276]) ).
fof(f2076,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,[],[f1417,f263]) ).
fof(f1417,plain,
! [X0,X1] :
( is_a_theorem(or(X1,and(X0,not(X1))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1134,f374]) ).
fof(f2065,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,[],[f324,f222]) ).
fof(f2064,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,[],[f324,f219]) ).
fof(f2063,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,implies(X2,necessarily(not(X0)))),implies(and(X2,possibly(X0)),X1))),
inference(superposition,[],[f324,f221]) ).
fof(f2062,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,[],[f324,f285]) ).
fof(f2059,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,X1)),implies(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f324,f279]) ).
fof(f2058,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(or(X2,implies(X0,X1))) ),
inference(resolution,[],[f324,f242]) ).
fof(f2071,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,[],[f2070,f218]) ).
fof(f2070,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,[],[f2056,f291]) ).
fof(f2056,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,[],[f324,f919]) ).
fof(f2069,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,[],[f2055,f291]) ).
fof(f2055,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(necessarily(or(X2,implies(X0,X1)))) ),
inference(resolution,[],[f324,f1594]) ).
fof(f2051,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,[],[f2050,f218]) ).
fof(f2050,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,[],[f2048,f219]) ).
fof(f2048,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,[],[f2027,f266]) ).
fof(f2049,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(strict_implies(not(necessarily(possibly(X0))),X1)) ),
inference(forward_demodulation,[],[f2047,f221]) ).
fof(f2047,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(necessarily(possibly(X0))),X1))
| ~ is_a_theorem(necessarily(not(necessarily(not(X0))))) ),
inference(superposition,[],[f2027,f245]) ).
fof(f2027,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1162,f228]) ).
fof(f2041,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,[],[f2033,f218]) ).
fof(f2033,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,[],[f1162,f264]) ).
fof(f2040,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,[],[f2032,f291]) ).
fof(f2032,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,[],[f1162,f276]) ).
fof(f2039,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,[],[f2031,f218]) ).
fof(f2031,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,[],[f1162,f263]) ).
fof(f1162,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(strict_implies(possibly(X0),X1)) ),
inference(forward_demodulation,[],[f1122,f218]) ).
fof(f1122,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(necessarily(implies(possibly(X0),X1))) ),
inference(resolution,[],[f919,f625]) ).
fof(f1891,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1842,f251]) ).
fof(f1957,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,[],[f323,f285]) ).
fof(f1946,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),not(not(X2))),or(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f326,f285]) ).
fof(f1945,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,[],[f855,f285]) ).
fof(f1942,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),not(X2)),implies(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f318,f285]) ).
fof(f1941,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,[],[f322,f285]) ).
fof(f1940,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,[],[f1842,f285]) ).
fof(f1937,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(not(X0),not(X1)))) ),
inference(superposition,[],[f1254,f285]) ).
fof(f1925,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X0),not(X1)))
| is_a_theorem(implies(or(X0,X1),X2)) ),
inference(superposition,[],[f251,f285]) ).
fof(f1919,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,[],[f758,f285]) ).
fof(f1918,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,[],[f916,f285]) ).
fof(f1917,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,[],[f1001,f285]) ).
fof(f1916,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,[],[f1147,f285]) ).
fof(f1912,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,[],[f285,f264]) ).
fof(f1911,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,[],[f285,f276]) ).
fof(f1910,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,[],[f285,f263]) ).
fof(f1909,plain,
! [X2,X3,X0,X1] : implies(or(X2,and(not(X0),not(X1))),X3) = or(and(not(X2),or(X0,X1)),X3),
inference(superposition,[],[f285,f222]) ).
fof(f1908,plain,
! [X2,X3,X0,X1] : implies(or(X2,and(X0,not(X1))),X3) = or(and(not(X2),implies(X0,X1)),X3),
inference(superposition,[],[f285,f219]) ).
fof(f1907,plain,
! [X2,X0,X1] : implies(or(X1,necessarily(not(X0))),X2) = or(and(not(X1),possibly(X0)),X2),
inference(superposition,[],[f285,f221]) ).
fof(f1906,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,[],[f285,f264]) ).
fof(f1963,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,[],[f1905,f284]) ).
fof(f1905,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,[],[f285,f276]) ).
fof(f1904,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,[],[f285,f263]) ).
fof(f1900,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,[],[f1842,f284]) ).
fof(f1899,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(X1)))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f1842,f283]) ).
fof(f1898,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,[],[f1842,f264]) ).
fof(f1897,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,[],[f1842,f276]) ).
fof(f1896,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,[],[f1842,f263]) ).
fof(f1895,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,[],[f1842,f222]) ).
fof(f1894,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,X1)))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1842,f219]) ).
fof(f1893,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1842,f221]) ).
fof(f1887,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,[],[f1881,f264]) ).
fof(f1886,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,[],[f1881,f276]) ).
fof(f1885,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,[],[f1881,f263]) ).
fof(f1884,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(or(X0,X1)))
| is_a_theorem(strict_implies(X2,and(not(X0),not(X1)))) ),
inference(superposition,[],[f1881,f222]) ).
fof(f1883,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,X1)))
| is_a_theorem(strict_implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f1881,f219]) ).
fof(f1882,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,necessarily(not(X0))))
| ~ is_a_theorem(not(possibly(X0))) ),
inference(superposition,[],[f1881,f221]) ).
fof(f1872,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,[],[f1867,f218]) ).
fof(f1867,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,[],[f1845,f264]) ).
fof(f1871,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,[],[f1866,f291]) ).
fof(f1866,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,[],[f1845,f276]) ).
fof(f1870,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,[],[f1865,f218]) ).
fof(f1865,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,[],[f1845,f263]) ).
fof(f1869,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,[],[f1864,f291]) ).
fof(f1864,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| is_a_theorem(strict_implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1845,f222]) ).
fof(f1868,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(forward_demodulation,[],[f1863,f218]) ).
fof(f1863,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1845,f219]) ).
fof(f1858,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,[],[f1155,f264]) ).
fof(f1857,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,[],[f1155,f276]) ).
fof(f1856,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,[],[f1155,f263]) ).
fof(f1855,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,[],[f1155,f222]) ).
fof(f1854,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,[],[f1155,f219]) ).
fof(f1853,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1155,f221]) ).
fof(f1852,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,[],[f1155,f264]) ).
fof(f1851,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,[],[f1155,f276]) ).
fof(f1850,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,[],[f1155,f263]) ).
fof(f1849,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,[],[f1155,f222]) ).
fof(f1848,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,[],[f1155,f219]) ).
fof(f1847,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(X0),not(X1)))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f1155,f221]) ).
fof(f1859,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1846,f279]) ).
fof(f1846,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(not(X1),not(X0))) ),
inference(resolution,[],[f1155,f247]) ).
fof(f1844,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X1),not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1155,f1242]) ).
fof(f1843,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),not(X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1155,f1253]) ).
fof(f1839,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,[],[f1147,f284]) ).
fof(f1838,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,[],[f1147,f283]) ).
fof(f1837,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,[],[f1147,f1139]) ).
fof(f1840,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,[],[f1834,f291]) ).
fof(f1834,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(or(X0,X0))) ),
inference(resolution,[],[f1147,f792]) ).
fof(f1831,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1139,f279]) ).
fof(f1833,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f1830,f279]) ).
fof(f1830,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(or(X0,implies(not(X0),X1))) ),
inference(resolution,[],[f1139,f376]) ).
fof(f1826,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1139,f1242]) ).
fof(f1825,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(implies(X0,X1),X0))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1139,f1253]) ).
fof(f1129,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(resolution,[],[f919,f405]) ).
fof(f1128,plain,
! [X0] :
( is_a_theorem(necessarily(strict_equiv(X0,X0)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X0))) ),
inference(resolution,[],[f919,f727]) ).
fof(f1816,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,[],[f1815,f218]) ).
fof(f1815,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,[],[f1096,f223]) ).
fof(f1814,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,[],[f1096,f220]) ).
fof(f1096,plain,
! [X0,X1] :
( is_a_theorem(necessarily(and(X1,X0)))
| ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f919,f253]) ).
fof(f1765,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,[],[f1182,f264]) ).
fof(f1792,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,[],[f1764,f218]) ).
fof(f1764,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,[],[f1181,f264]) ).
fof(f1763,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,[],[f1137,f264]) ).
fof(f1758,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,[],[f855,f264]) ).
fof(f1756,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,[],[f729,f264]) ).
fof(f1755,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,[],[f720,f264]) ).
fof(f1754,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f716,f264]) ).
fof(f1788,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,[],[f1753,f218]) ).
fof(f1753,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,[],[f625,f264]) ).
fof(f1750,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,[],[f400,f264]) ).
fof(f1749,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,[],[f400,f264]) ).
fof(f1748,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,[],[f382,f264]) ).
fof(f1747,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,[],[f378,f264]) ).
fof(f1746,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,[],[f376,f264]) ).
fof(f1745,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,[],[f374,f264]) ).
fof(f1739,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,[],[f343,f264]) ).
fof(f1785,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,[],[f1738,f218]) ).
fof(f1738,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,[],[f332,f264]) ).
fof(f1737,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,[],[f326,f264]) ).
fof(f1735,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,[],[f322,f264]) ).
fof(f1783,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,[],[f1733,f218]) ).
fof(f1733,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,[],[f315,f264]) ).
fof(f1782,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,[],[f1732,f218]) ).
fof(f1732,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,[],[f312,f264]) ).
fof(f1781,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,[],[f1731,f218]) ).
fof(f1731,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,[],[f309,f264]) ).
fof(f1780,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,[],[f1730,f218]) ).
fof(f1730,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,[],[f305,f264]) ).
fof(f1729,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),necessarily(possibly(implies(X0,and(X1,not(X2))))))),
inference(superposition,[],[f304,f264]) ).
fof(f1728,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),or(implies(X0,and(X1,not(X2))),X3))),
inference(superposition,[],[f303,f264]) ).
fof(f1727,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),or(X3,implies(X0,and(X1,not(X2)))))),
inference(superposition,[],[f302,f264]) ).
fof(f1726,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,[],[f301,f264]) ).
fof(f1725,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,[],[f300,f264]) ).
fof(f1724,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,[],[f299,f264]) ).
fof(f1723,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),implies(X3,implies(X0,and(X1,not(X2)))))),
inference(superposition,[],[f298,f264]) ).
fof(f1722,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,[],[f296,f264]) ).
fof(f1721,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,[],[f294,f264]) ).
fof(f1720,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,[],[f293,f264]) ).
fof(f1719,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,[],[f284,f264]) ).
fof(f1779,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,[],[f1718,f218]) ).
fof(f1718,plain,
! [X2,X3,X0,X1] : implies(possibly(and(X0,implies(X1,X2))),X3) = or(necessarily(implies(X0,and(X1,not(X2)))),X3),
inference(superposition,[],[f283,f264]) ).
fof(f1717,plain,
! [X2,X3,X0,X1] : implies(implies(X0,and(X1,not(X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(superposition,[],[f279,f264]) ).
fof(f1716,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,[],[f276,f264]) ).
fof(f1715,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(f1778,plain,
! [X2,X0,X1] : not(necessarily(possibly(and(X0,implies(X1,X2))))) = possibly(strict_implies(X0,and(X1,not(X2)))),
inference(forward_demodulation,[],[f1714,f218]) ).
fof(f1714,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(f1713,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(f1712,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(f1777,plain,
! [X2,X0,X1] : not(strict_implies(X0,and(X1,not(X2)))) = possibly(and(X0,implies(X1,X2))),
inference(forward_demodulation,[],[f1711,f218]) ).
fof(f1711,plain,
! [X2,X0,X1] : possibly(and(X0,implies(X1,X2))) = not(necessarily(implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f221,f264]) ).
fof(f1710,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(f1705,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
inference(superposition,[],[f264,f279]) ).
fof(f1643,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X1,X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1594,f406]) ).
fof(f1642,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1594,f405]) ).
fof(f1699,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1636,f1240]) ).
fof(f1698,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X1,X0))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1636,f1251]) ).
fof(f1636,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1594,f248]) ).
fof(f1621,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1594,f236]) ).
fof(f1695,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),or(X0,X1)))
| ~ is_a_theorem(or(X0,X2)) ),
inference(forward_demodulation,[],[f1691,f279]) ).
fof(f1691,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X2,X1),or(X0,X1)))
| ~ is_a_theorem(implies(not(X0),X2)) ),
inference(superposition,[],[f695,f279]) ).
fof(f1690,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,not(X0))) ),
inference(superposition,[],[f695,f279]) ).
fof(f1694,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,[],[f1693,f218]) ).
fof(f1693,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,[],[f1687,f218]) ).
fof(f1687,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,[],[f695,f919]) ).
fof(f1692,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,[],[f1686,f218]) ).
fof(f1686,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,[],[f695,f1594]) ).
fof(f1620,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X1,X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1594,f235]) ).
fof(f1682,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,[],[f1681,f218]) ).
fof(f1681,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1607,f223]) ).
fof(f1680,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,[],[f1607,f220]) ).
fof(f1607,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1594,f253]) ).
fof(f1668,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f1625,f223]) ).
fof(f1667,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f1625,f220]) ).
fof(f1625,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X1,X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1594,f233]) ).
fof(f1664,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1624,f223]) ).
fof(f1663,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f1624,f220]) ).
fof(f1624,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1594,f232]) ).
fof(f1660,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f1631,f291]) ).
fof(f1659,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1631,f218]) ).
fof(f1631,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1594,f225]) ).
fof(f1640,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1594,f296]) ).
fof(f1638,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,[],[f1594,f407]) ).
fof(f1637,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(resolution,[],[f1594,f505]) ).
fof(f1635,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(resolution,[],[f1594,f332]) ).
fof(f1634,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(resolution,[],[f1594,f625]) ).
fof(f1633,plain,
! [X0,X1] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(necessarily(X1)))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f1594,f551]) ).
fof(f1656,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),possibly(X0)))
| is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(forward_demodulation,[],[f1630,f291]) ).
fof(f1630,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(or(X1,possibly(X0)))) ),
inference(resolution,[],[f1594,f323]) ).
fof(f1655,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f1629,f291]) ).
fof(f1629,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(or(X0,or(X0,X1)))) ),
inference(resolution,[],[f1594,f357]) ).
fof(f1654,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f1628,f291]) ).
fof(f1628,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(or(X1,not(not(X0))))) ),
inference(resolution,[],[f1594,f326]) ).
fof(f1652,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),X1))
| is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1626,f291]) ).
fof(f1626,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(or(X1,X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f1594,f916]) ).
fof(f1623,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1594,f294]) ).
fof(f1622,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X1,not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1594,f293]) ).
fof(f1651,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,[],[f1619,f218]) ).
fof(f1619,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1594,f575]) ).
fof(f1650,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(forward_demodulation,[],[f1617,f218]) ).
fof(f1617,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f1594,f758]) ).
fof(f1649,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,[],[f1616,f218]) ).
fof(f1616,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,[],[f1594,f244]) ).
fof(f1648,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,X0))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) ),
inference(forward_demodulation,[],[f1615,f218]) ).
fof(f1615,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(necessarily(implies(X2,X0))) ),
inference(resolution,[],[f1594,f243]) ).
fof(f1647,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| is_a_theorem(implies(implies(X0,X1),equiv(X1,X0))) ),
inference(forward_demodulation,[],[f1614,f218]) ).
fof(f1614,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
| ~ is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f1594,f240]) ).
fof(f1646,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1613,f218]) ).
fof(f1613,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(implies(X0,implies(X0,X1)))) ),
inference(resolution,[],[f1594,f238]) ).
fof(f1610,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1594,f301]) ).
fof(f1606,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1594,f1416]) ).
fof(f1599,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,[],[f1001,f284]) ).
fof(f1598,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,[],[f1001,f283]) ).
fof(f1595,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1001,f1170]) ).
fof(f1571,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),equiv(X1,not(X0))))
| ~ is_a_theorem(implies(X1,not(X0))) ),
inference(superposition,[],[f575,f279]) ).
fof(f1572,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,[],[f1568,f218]) ).
fof(f1568,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,[],[f575,f919]) ).
fof(f1468,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,[],[f1467,f218]) ).
fof(f1467,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f1434,f223]) ).
fof(f1466,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,[],[f1434,f220]) ).
fof(f1251,plain,
! [X0,X1] :
( is_a_theorem(necessarily(strict_implies(X1,X0)))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(superposition,[],[f1244,f220]) ).
fof(f1240,plain,
! [X0,X1] :
( is_a_theorem(necessarily(strict_implies(X0,X1)))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(superposition,[],[f1233,f220]) ).
fof(f1198,plain,
! [X0] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X0)))
| is_a_theorem(strict_equiv(X0,X0)) ),
inference(superposition,[],[f1186,f220]) ).
fof(f1444,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,[],[f1182,f276]) ).
fof(f1443,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,[],[f1182,f263]) ).
fof(f1182,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1170,f855]) ).
fof(f1437,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f1416,f279]) ).
fof(f1438,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1436,f218]) ).
fof(f1436,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1416,f223]) ).
fof(f1435,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,[],[f1416,f220]) ).
fof(f1432,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(necessarily(and(X0,X1))) ),
inference(resolution,[],[f1416,f919]) ).
fof(f1150,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1109,f218]) ).
fof(f1109,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f919,f236]) ).
fof(f1149,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(forward_demodulation,[],[f1108,f218]) ).
fof(f1108,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f919,f235]) ).
fof(f1148,plain,
! [X0] :
( is_a_theorem(necessarily(equiv(X0,X0)))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(forward_demodulation,[],[f1107,f218]) ).
fof(f1107,plain,
! [X0] :
( ~ is_a_theorem(necessarily(implies(X0,X0)))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(resolution,[],[f919,f705]) ).
fof(f1424,plain,
! [X0,X1] :
( is_a_theorem(implies(strict_implies(X0,X1),strict_equiv(X1,X0)))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f407,f242]) ).
fof(f1425,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,[],[f1422,f218]) ).
fof(f1422,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,[],[f407,f919]) ).
fof(f1420,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1419,f218]) ).
fof(f1419,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1134,f223]) ).
fof(f1418,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,[],[f1134,f220]) ).
fof(f1414,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(and(X0,X1)))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1134,f792]) ).
fof(f1373,plain,
~ is_a_theorem(equiv(necessarily(possibly(sK0)),possibly(sK0))),
inference(resolution,[],[f1253,f224]) ).
fof(f1374,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1253,f792]) ).
fof(f1253,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(forward_demodulation,[],[f1252,f218]) ).
fof(f1252,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(superposition,[],[f1244,f223]) ).
fof(f1367,plain,
~ is_a_theorem(equiv(possibly(sK0),necessarily(possibly(sK0)))),
inference(resolution,[],[f1242,f224]) ).
fof(f1368,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1242,f792]) ).
fof(f1242,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(forward_demodulation,[],[f1241,f218]) ).
fof(f1241,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1233,f223]) ).
fof(f1351,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,[],[f1347,f291]) ).
fof(f1347,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,[],[f1181,f276]) ).
fof(f1350,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,[],[f1346,f218]) ).
fof(f1346,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,necessarily(not(X1)))))
| is_a_theorem(implies(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f1181,f263]) ).
fof(f1349,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,[],[f1345,f291]) ).
fof(f1345,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| is_a_theorem(implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1181,f222]) ).
fof(f1348,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(forward_demodulation,[],[f1344,f218]) ).
fof(f1344,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1181,f219]) ).
fof(f1343,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(possibly(X0))) ),
inference(superposition,[],[f1181,f221]) ).
fof(f1341,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(possibly(X0)),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1181,f331]) ).
fof(f1181,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1170,f322]) ).
fof(f1304,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),not(not(X2))),or(X2,and(X0,not(X1))))),
inference(superposition,[],[f326,f284]) ).
fof(f1303,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,[],[f855,f284]) ).
fof(f1296,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1254,f284]) ).
fof(f1284,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f251,f284]) ).
fof(f1278,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,[],[f758,f284]) ).
fof(f1277,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,[],[f916,f284]) ).
fof(f1275,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,[],[f284,f276]) ).
fof(f1274,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(X0,possibly(X1))),X3) = or(and(X2,implies(X0,necessarily(not(X1)))),X3),
inference(superposition,[],[f284,f263]) ).
fof(f1273,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(not(X0),not(X1))),X3) = or(and(X2,or(X0,X1)),X3),
inference(superposition,[],[f284,f222]) ).
fof(f1272,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(X0,not(X1))),X3) = or(and(X2,implies(X0,X1)),X3),
inference(superposition,[],[f284,f219]) ).
fof(f1271,plain,
! [X2,X0,X1] : implies(implies(X1,necessarily(not(X0))),X2) = or(and(X1,possibly(X0)),X2),
inference(superposition,[],[f284,f221]) ).
fof(f1263,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,[],[f1137,f276]) ).
fof(f1262,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,[],[f1137,f263]) ).
fof(f1261,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(or(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(not(X0),not(X1)))) ),
inference(superposition,[],[f1137,f222]) ).
fof(f1260,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1137,f219]) ).
fof(f1259,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1137,f221]) ).
fof(f1264,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1258,f279]) ).
fof(f1258,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[],[f1137,f261]) ).
fof(f1244,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X1,X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1113,f228]) ).
fof(f1247,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1246,f218]) ).
fof(f1246,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(superposition,[],[f1113,f223]) ).
fof(f1245,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X1,X0))) ),
inference(superposition,[],[f1113,f220]) ).
fof(f1113,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f919,f233]) ).
fof(f1233,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1112,f228]) ).
fof(f1236,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1235,f218]) ).
fof(f1235,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1112,f223]) ).
fof(f1234,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(superposition,[],[f1112,f220]) ).
fof(f1112,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f919,f232]) ).
fof(f1218,plain,
! [X0,X1] :
( is_a_theorem(not(strict_implies(X0,X1)))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1210,f266]) ).
fof(f1217,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(not(necessarily(possibly(X0)))) ),
inference(superposition,[],[f1210,f245]) ).
fof(f1210,plain,
! [X0] :
( is_a_theorem(possibly(X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1203,f258]) ).
fof(f1212,plain,
! [X0,X1] :
( is_a_theorem(necessarily(not(strict_implies(X0,X1))))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1203,f266]) ).
fof(f1211,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1203,f245]) ).
fof(f1203,plain,
! [X0] :
( is_a_theorem(necessarily(possibly(X0)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1101,f258]) ).
fof(f1201,plain,
~ is_a_theorem(necessarily(sK0)),
inference(resolution,[],[f1101,f1166]) ).
fof(f1205,plain,
! [X0,X1] :
( is_a_theorem(necessarily(necessarily(not(strict_implies(X0,X1)))))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1101,f266]) ).
fof(f1204,plain,
! [X0] :
( is_a_theorem(necessarily(necessarily(not(necessarily(possibly(X0))))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1101,f245]) ).
fof(f1101,plain,
! [X0] :
( is_a_theorem(necessarily(necessarily(possibly(X0))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f919,f226]) ).
fof(f1186,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1097,f258]) ).
fof(f1189,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(forward_demodulation,[],[f1188,f218]) ).
fof(f1188,plain,
! [X0] :
( is_a_theorem(necessarily(equiv(X0,X0)))
| ~ is_a_theorem(necessarily(implies(X0,X0))) ),
inference(superposition,[],[f1097,f223]) ).
fof(f1187,plain,
! [X0] :
( is_a_theorem(necessarily(strict_equiv(X0,X0)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X0))) ),
inference(superposition,[],[f1097,f220]) ).
fof(f1097,plain,
! [X0] :
( is_a_theorem(necessarily(and(X0,X0)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f919,f702]) ).
fof(f1178,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f1169,f279]) ).
fof(f1166,plain,
~ is_a_theorem(necessarily(necessarily(possibly(sK0)))),
inference(resolution,[],[f1133,f224]) ).
fof(f1132,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f919,f279]) ).
fof(f1164,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(forward_demodulation,[],[f1125,f218]) ).
fof(f1125,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(necessarily(implies(necessarily(X0),necessarily(X1)))) ),
inference(resolution,[],[f919,f505]) ).
fof(f1123,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(necessarily(necessarily(not(necessarily(possibly(X0)))))) ),
inference(resolution,[],[f919,f332]) ).
fof(f1121,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(necessarily(necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f919,f551]) ).
fof(f1161,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(X1)),X0))
| ~ is_a_theorem(strict_implies(not(X0),possibly(X1))) ),
inference(forward_demodulation,[],[f1160,f218]) ).
fof(f1160,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),possibly(X1)))
| is_a_theorem(necessarily(implies(necessarily(not(X1)),X0))) ),
inference(forward_demodulation,[],[f1118,f291]) ).
fof(f1118,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,possibly(X1))))
| is_a_theorem(necessarily(implies(necessarily(not(X1)),X0))) ),
inference(resolution,[],[f919,f323]) ).
fof(f1159,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(strict_implies(not(X0),or(X0,X1))) ),
inference(forward_demodulation,[],[f1158,f291]) ).
fof(f1158,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(forward_demodulation,[],[f1117,f291]) ).
fof(f1117,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,or(X0,X1))))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f919,f357]) ).
fof(f1157,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(strict_implies(not(X0),not(not(X1)))) ),
inference(forward_demodulation,[],[f1156,f291]) ).
fof(f1156,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(not(X1))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(forward_demodulation,[],[f1116,f291]) ).
fof(f1116,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,not(not(X1)))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f919,f326]) ).
fof(f1153,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,[],[f1114,f291]) ).
fof(f1114,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X0)))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f919,f916]) ).
fof(f1152,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(necessarily(equiv(not(X0),X1))) ),
inference(forward_demodulation,[],[f1111,f291]) ).
fof(f1111,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(not(X0),X1)))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f919,f294]) ).
fof(f1151,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(necessarily(equiv(X0,not(X1)))) ),
inference(forward_demodulation,[],[f1110,f291]) ).
fof(f1110,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,not(X1))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f919,f293]) ).
fof(f1145,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,[],[f1144,f218]) ).
fof(f1144,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,[],[f1105,f218]) ).
fof(f1105,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,[],[f919,f244]) ).
fof(f1143,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,[],[f1142,f218]) ).
fof(f1142,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,[],[f1104,f218]) ).
fof(f1104,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(implies(X1,X2),implies(X0,X2)))) ),
inference(resolution,[],[f919,f243]) ).
fof(f1141,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1140,f218]) ).
fof(f1140,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(forward_demodulation,[],[f1103,f218]) ).
fof(f1103,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(resolution,[],[f919,f240]) ).
fof(f1136,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),and(X0,not(X1))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1099,f291]) ).
fof(f1099,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X1,and(X0,not(X1))))) ),
inference(resolution,[],[f919,f301]) ).
fof(f1135,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1098,f291]) ).
fof(f1098,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f919,f229]) ).
fof(f1058,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,[],[f855,f276]) ).
fof(f1056,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,[],[f729,f276]) ).
fof(f1055,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,or(X0,necessarily(not(X1)))),implies(X2,and(not(X0),possibly(X1))))),
inference(superposition,[],[f720,f276]) ).
fof(f1054,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(X0,necessarily(not(X1))))),
inference(superposition,[],[f716,f276]) ).
fof(f1084,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,[],[f1053,f291]) ).
fof(f1053,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(or(X0,necessarily(not(X1)))),implies(possibly(and(not(X0),possibly(X1))),X2))),
inference(superposition,[],[f625,f276]) ).
fof(f1050,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,[],[f400,f276]) ).
fof(f1049,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,[],[f400,f276]) ).
fof(f1048,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,[],[f382,f276]) ).
fof(f1047,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,[],[f378,f276]) ).
fof(f1046,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,[],[f376,f276]) ).
fof(f1045,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,[],[f374,f276]) ).
fof(f1041,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,[],[f343,f276]) ).
fof(f1081,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,[],[f1040,f291]) ).
fof(f1040,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(or(X0,necessarily(not(X1)))),necessarily(not(necessarily(possibly(and(not(X0),possibly(X1)))))))),
inference(superposition,[],[f332,f276]) ).
fof(f1039,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,[],[f326,f276]) ).
fof(f1080,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,[],[f1038,f291]) ).
fof(f1038,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,[],[f323,f276]) ).
fof(f1037,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,[],[f322,f276]) ).
fof(f1079,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,[],[f1035,f291]) ).
fof(f1035,plain,
! [X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),necessarily(possibly(possibly(and(not(X0),possibly(X1))))))),
inference(superposition,[],[f315,f276]) ).
fof(f1078,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,[],[f1034,f291]) ).
fof(f1034,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),or(possibly(and(not(X0),possibly(X1))),X2))),
inference(superposition,[],[f312,f276]) ).
fof(f1077,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,[],[f1033,f291]) ).
fof(f1033,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),or(X2,possibly(and(not(X0),possibly(X1)))))),
inference(superposition,[],[f309,f276]) ).
fof(f1076,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,[],[f1032,f291]) ).
fof(f1032,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),implies(X2,possibly(and(not(X0),possibly(X1)))))),
inference(superposition,[],[f305,f276]) ).
fof(f1031,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),necessarily(possibly(or(X0,necessarily(not(X1))))))),
inference(superposition,[],[f304,f276]) ).
fof(f1030,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(or(X0,necessarily(not(X1))),X2))),
inference(superposition,[],[f303,f276]) ).
fof(f1029,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(X2,or(X0,necessarily(not(X1)))))),
inference(superposition,[],[f302,f276]) ).
fof(f1028,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(not(X0),possibly(X1)),and(X2,or(X0,necessarily(not(X1))))))),
inference(superposition,[],[f301,f276]) ).
fof(f1027,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,[],[f300,f276]) ).
fof(f1026,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),implies(X2,and(or(X0,necessarily(not(X1))),X2)))),
inference(superposition,[],[f299,f276]) ).
fof(f1025,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),implies(X2,or(X0,necessarily(not(X1)))))),
inference(superposition,[],[f298,f276]) ).
fof(f1024,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,[],[f296,f276]) ).
fof(f1023,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(or(X0,necessarily(not(X1))),X2),or(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f294,f276]) ).
fof(f1022,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,or(X0,necessarily(not(X1)))),or(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f293,f276]) ).
fof(f1075,plain,
! [X2,X0,X1] : implies(possibly(and(not(X0),possibly(X1))),X2) = or(strict_implies(not(X0),necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f1021,f291]) ).
fof(f1021,plain,
! [X2,X0,X1] : implies(possibly(and(not(X0),possibly(X1))),X2) = or(necessarily(or(X0,necessarily(not(X1)))),X2),
inference(superposition,[],[f283,f276]) ).
fof(f1020,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = implies(or(X0,necessarily(not(X1))),X2),
inference(superposition,[],[f279,f276]) ).
fof(f1019,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(not(X0),possibly(X1)))) = possibly(and(X2,or(X0,necessarily(not(X1))))),
inference(superposition,[],[f266,f276]) ).
fof(f1074,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),possibly(X1))))) = possibly(strict_implies(not(X0),necessarily(not(X1)))),
inference(forward_demodulation,[],[f1018,f291]) ).
fof(f1018,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),possibly(X1))))) = possibly(necessarily(or(X0,necessarily(not(X1))))),
inference(superposition,[],[f245,f276]) ).
fof(f1073,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = implies(or(X0,necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f1017,f219]) ).
fof(f1017,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = not(and(or(X0,necessarily(not(X1))),not(X2))),
inference(superposition,[],[f222,f276]) ).
fof(f1016,plain,
! [X2,X0,X1] : or(X2,and(not(X0),possibly(X1))) = not(and(not(X2),or(X0,necessarily(not(X1))))),
inference(superposition,[],[f222,f276]) ).
fof(f1072,plain,
! [X0,X1] : possibly(and(not(X0),possibly(X1))) = not(strict_implies(not(X0),necessarily(not(X1)))),
inference(forward_demodulation,[],[f1015,f291]) ).
fof(f1015,plain,
! [X0,X1] : possibly(and(not(X0),possibly(X1))) = not(necessarily(or(X0,necessarily(not(X1))))),
inference(superposition,[],[f221,f276]) ).
fof(f1014,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),possibly(X1))) = not(and(X2,or(X0,necessarily(not(X1))))),
inference(superposition,[],[f219,f276]) ).
fof(f1066,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,[],[f1008,f263]) ).
fof(f1008,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),necessarily(not(X2))) = not(and(or(X0,necessarily(not(X1))),possibly(X2))),
inference(superposition,[],[f276,f276]) ).
fof(f1007,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),necessarily(not(X2))) = not(and(implies(X0,necessarily(not(X1))),possibly(X2))),
inference(superposition,[],[f276,f263]) ).
fof(f1065,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),necessarily(not(X2))) = implies(or(X0,X1),necessarily(not(X2))),
inference(forward_demodulation,[],[f1006,f263]) ).
fof(f1006,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),necessarily(not(X2))) = not(and(or(X0,X1),possibly(X2))),
inference(superposition,[],[f276,f222]) ).
fof(f1064,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),necessarily(not(X2))) = implies(implies(X0,X1),necessarily(not(X2))),
inference(forward_demodulation,[],[f1005,f263]) ).
fof(f1005,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),necessarily(not(X2))) = not(and(implies(X0,X1),possibly(X2))),
inference(superposition,[],[f276,f219]) ).
fof(f1003,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(possibly(X0),necessarily(not(X0))),X1))
| ~ is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f916,f283]) ).
fof(f1002,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(or(X0,X0),X1)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(resolution,[],[f916,f354]) ).
fof(f998,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(not(X1))))
| is_a_theorem(or(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f855,f283]) ).
fof(f997,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,[],[f855,f263]) ).
fof(f996,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,[],[f855,f222]) ).
fof(f995,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,not(implies(X0,X1))))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f855,f219]) ).
fof(f585,plain,
! [X0,X1] :
( is_a_theorem(not(strict_implies(X0,X1)))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f262,f266]) ).
fof(f938,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(or(X1,possibly(X0))) ),
inference(resolution,[],[f323,f242]) ).
fof(f930,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(X0,possibly(X1)),and(not(X2),implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f400,f263]) ).
fof(f929,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(not(X0),not(X1)),and(not(X2),or(X0,X1))))),
inference(superposition,[],[f400,f222]) ).
fof(f928,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(X0,not(X1)),and(not(X2),implies(X0,X1))))),
inference(superposition,[],[f400,f219]) ).
fof(f926,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(X2,and(implies(X0,necessarily(not(X1))),not(X2))))),
inference(superposition,[],[f400,f263]) ).
fof(f925,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X2,and(or(X0,X1),not(X2))))),
inference(superposition,[],[f400,f222]) ).
fof(f924,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(X2,and(implies(X0,X1),not(X2))))),
inference(superposition,[],[f400,f219]) ).
fof(f920,plain,
! [X0,X1] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(not(X1)))
| ~ is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f792,f376]) ).
fof(f918,plain,
! [X0,X1] : is_a_theorem(implies(implies(necessarily(not(X0)),X1),implies(implies(possibly(X0),necessarily(not(X0))),X1))),
inference(superposition,[],[f758,f283]) ).
fof(f917,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),implies(or(not(X0),not(X0)),X1))),
inference(superposition,[],[f758,f279]) ).
fof(f899,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,or(X0,X1))) ),
inference(resolution,[],[f357,f242]) ).
fof(f892,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,necessarily(not(X1))),necessarily(not(necessarily(possibly(and(X0,possibly(X1)))))))),
inference(forward_demodulation,[],[f880,f218]) ).
fof(f880,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,necessarily(not(X1)))),necessarily(not(necessarily(possibly(and(X0,possibly(X1)))))))),
inference(superposition,[],[f332,f263]) ).
fof(f331,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f249,f245]) ).
fof(f860,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),not(not(X1))),or(X1,necessarily(not(X0))))),
inference(superposition,[],[f326,f283]) ).
fof(f859,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(implies(X0,necessarily(not(X1))))),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f326,f263]) ).
fof(f858,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(or(X0,X1))),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f326,f222]) ).
fof(f857,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(implies(X0,X1))),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f326,f219]) ).
fof(f838,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),and(implies(X0,necessarily(not(X1))),implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f729,f263]) ).
fof(f837,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,implies(X0,necessarily(not(X1)))),implies(X2,and(X0,possibly(X1))))),
inference(superposition,[],[f720,f263]) ).
fof(f836,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f716,f263]) ).
fof(f852,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X0,necessarily(not(X1))),implies(possibly(and(X0,possibly(X1))),X2))),
inference(forward_demodulation,[],[f835,f218]) ).
fof(f835,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(implies(X0,necessarily(not(X1)))),implies(possibly(and(X0,possibly(X1))),X2))),
inference(superposition,[],[f625,f263]) ).
fof(f832,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,[],[f382,f263]) ).
fof(f831,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,[],[f378,f263]) ).
fof(f830,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,[],[f376,f263]) ).
fof(f829,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,[],[f374,f263]) ).
fof(f825,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,necessarily(not(X1)))))
| is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f343,f263]) ).
fof(f824,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,[],[f322,f263]) ).
fof(f849,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),necessarily(possibly(possibly(and(X0,possibly(X1))))))),
inference(forward_demodulation,[],[f822,f218]) ).
fof(f822,plain,
! [X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),necessarily(possibly(possibly(and(X0,possibly(X1))))))),
inference(superposition,[],[f315,f263]) ).
fof(f848,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),or(possibly(and(X0,possibly(X1))),X2))),
inference(forward_demodulation,[],[f821,f218]) ).
fof(f821,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),or(possibly(and(X0,possibly(X1))),X2))),
inference(superposition,[],[f312,f263]) ).
fof(f847,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),or(X2,possibly(and(X0,possibly(X1)))))),
inference(forward_demodulation,[],[f820,f218]) ).
fof(f820,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),or(X2,possibly(and(X0,possibly(X1)))))),
inference(superposition,[],[f309,f263]) ).
fof(f846,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),implies(X2,possibly(and(X0,possibly(X1)))))),
inference(forward_demodulation,[],[f819,f218]) ).
fof(f819,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),implies(X2,possibly(and(X0,possibly(X1)))))),
inference(superposition,[],[f305,f263]) ).
fof(f818,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),necessarily(possibly(implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f304,f263]) ).
fof(f817,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(implies(X0,necessarily(not(X1))),X2))),
inference(superposition,[],[f303,f263]) ).
fof(f816,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(X2,implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f302,f263]) ).
fof(f815,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(X0,possibly(X1)),and(X2,implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f301,f263]) ).
fof(f814,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,[],[f300,f263]) ).
fof(f813,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X2,and(implies(X0,necessarily(not(X1))),X2)))),
inference(superposition,[],[f299,f263]) ).
fof(f812,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X2,implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f298,f263]) ).
fof(f811,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,necessarily(not(X1))),X2),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f296,f263]) ).
fof(f810,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(implies(X0,necessarily(not(X1))),X2),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f294,f263]) ).
fof(f809,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,implies(X0,necessarily(not(X1)))),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f293,f263]) ).
fof(f845,plain,
! [X2,X0,X1] : implies(possibly(and(X0,possibly(X1))),X2) = or(strict_implies(X0,necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f808,f218]) ).
fof(f808,plain,
! [X2,X0,X1] : implies(possibly(and(X0,possibly(X1))),X2) = or(necessarily(implies(X0,necessarily(not(X1)))),X2),
inference(superposition,[],[f283,f263]) ).
fof(f807,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),X2) = implies(implies(X0,necessarily(not(X1))),X2),
inference(superposition,[],[f279,f263]) ).
fof(f806,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(f844,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,possibly(X1))))) = possibly(strict_implies(X0,necessarily(not(X1)))),
inference(forward_demodulation,[],[f805,f218]) ).
fof(f805,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,possibly(X1))))) = possibly(necessarily(implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f245,f263]) ).
fof(f804,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),X2) = not(and(implies(X0,necessarily(not(X1))),not(X2))),
inference(superposition,[],[f222,f263]) ).
fof(f803,plain,
! [X2,X0,X1] : or(X2,and(X0,possibly(X1))) = not(and(not(X2),implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f222,f263]) ).
fof(f843,plain,
! [X0,X1] : not(strict_implies(X0,necessarily(not(X1)))) = possibly(and(X0,possibly(X1))),
inference(forward_demodulation,[],[f802,f218]) ).
fof(f802,plain,
! [X0,X1] : possibly(and(X0,possibly(X1))) = not(necessarily(implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f221,f263]) ).
fof(f801,plain,
! [X2,X0,X1] : implies(X2,and(X0,possibly(X1))) = not(and(X2,implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f219,f263]) ).
fof(f796,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,[],[f551,f291]) ).
fof(f795,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,[],[f551,f218]) ).
fof(f794,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,[],[f551,f291]) ).
fof(f793,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,[],[f551,f218]) ).
fof(f789,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X0,X1))),
inference(superposition,[],[f720,f279]) ).
fof(f788,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,or(X0,X1)),implies(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f720,f222]) ).
fof(f787,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,implies(X0,X1)),implies(X2,and(X0,not(X1))))),
inference(superposition,[],[f720,f219]) ).
fof(f786,plain,
! [X0,X1] : is_a_theorem(or(and(X1,possibly(X0)),implies(X1,necessarily(not(X0))))),
inference(superposition,[],[f720,f221]) ).
fof(f736,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(superposition,[],[f726,f220]) ).
fof(f769,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),and(or(X0,X1),or(X0,X1)))),
inference(superposition,[],[f729,f222]) ).
fof(f768,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),and(implies(X0,X1),implies(X0,X1)))),
inference(superposition,[],[f729,f219]) ).
fof(f765,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(resolution,[],[f727,f242]) ).
fof(f760,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(f728,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f702,f223]) ).
fof(f721,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X0,X1))),
inference(superposition,[],[f716,f222]) ).
fof(f713,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,or(X0,X1))) ),
inference(forward_demodulation,[],[f712,f279]) ).
fof(f712,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f709,f279]) ).
fof(f709,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,implies(not(X0),X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f354,f279]) ).
fof(f706,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),implies(X0,X0))),
inference(resolution,[],[f354,f243]) ).
fof(f700,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X2),implies(implies(X2,X1),or(X0,X1)))),
inference(forward_demodulation,[],[f698,f279]) ).
fof(f698,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X0),X2),implies(implies(X2,X1),or(X0,X1)))),
inference(superposition,[],[f243,f279]) ).
fof(f693,plain,
~ is_a_theorem(not(sK0)),
inference(resolution,[],[f683,f228]) ).
fof(f683,plain,
~ is_a_theorem(necessarily(not(sK0))),
inference(resolution,[],[f627,f268]) ).
fof(f627,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f251,f283]) ).
fof(f664,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f625,f242]) ).
fof(f584,plain,
! [X0,X1] :
( is_a_theorem(necessarily(not(strict_implies(X0,X1))))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f249,f266]) ).
fof(f582,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(not(X0),not(X1)))) = possibly(and(X2,or(X0,X1))),
inference(superposition,[],[f266,f222]) ).
fof(f581,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(X0,not(X1)))) = possibly(and(X2,implies(X0,X1))),
inference(superposition,[],[f266,f219]) ).
fof(f580,plain,
! [X0,X1] : not(strict_implies(X1,necessarily(not(X0)))) = possibly(and(X1,possibly(X0))),
inference(superposition,[],[f266,f221]) ).
fof(f555,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,or(X0,X1)),implies(necessarily(X2),strict_implies(not(X0),X1)))),
inference(superposition,[],[f505,f291]) ).
fof(f553,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),implies(strict_implies(not(X0),X1),necessarily(X2)))),
inference(superposition,[],[f505,f291]) ).
fof(f500,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(or(X0,X1),X2))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f382,f222]) ).
fof(f499,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(implies(X0,X1),X2))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f382,f219]) ).
fof(f498,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(possibly(X0),X1))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f382,f221]) ).
fof(f382,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f294,f242]) ).
fof(f497,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X2,or(X0,X1)))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f378,f222]) ).
fof(f496,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X2,implies(X0,X1)))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f378,f219]) ).
fof(f495,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X1,possibly(X0)))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f378,f221]) ).
fof(f378,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X1,not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f293,f242]) ).
fof(f493,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,[],[f376,f222]) ).
fof(f492,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,X1),X2))
| ~ is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f376,f219]) ).
fof(f491,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f376,f221]) ).
fof(f487,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,[],[f374,f222]) ).
fof(f486,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f374,f219]) ).
fof(f485,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(X0),X1))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f374,f221]) ).
fof(f330,plain,
! [X0] :
( is_a_theorem(not(necessarily(possibly(X0))))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f262,f245]) ).
fof(f468,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f287,f223]) ).
fof(f465,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f253,f223]) ).
fof(f464,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(superposition,[],[f234,f223]) ).
fof(f458,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),necessarily(possibly(possibly(and(not(X0),not(X1))))))),
inference(forward_demodulation,[],[f453,f291]) ).
fof(f453,plain,
! [X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),necessarily(possibly(possibly(and(not(X0),not(X1))))))),
inference(superposition,[],[f315,f222]) ).
fof(f457,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(X0,X1),necessarily(possibly(possibly(and(X0,not(X1))))))),
inference(forward_demodulation,[],[f452,f218]) ).
fof(f452,plain,
! [X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),necessarily(possibly(possibly(and(X0,not(X1))))))),
inference(superposition,[],[f315,f219]) ).
fof(f448,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),or(possibly(and(not(X0),not(X1))),X2))),
inference(forward_demodulation,[],[f443,f291]) ).
fof(f443,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),or(possibly(and(not(X0),not(X1))),X2))),
inference(superposition,[],[f312,f222]) ).
fof(f447,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),or(possibly(and(X0,not(X1))),X2))),
inference(forward_demodulation,[],[f442,f218]) ).
fof(f442,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),or(possibly(and(X0,not(X1))),X2))),
inference(superposition,[],[f312,f219]) ).
fof(f438,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),or(X2,possibly(and(not(X0),not(X1)))))),
inference(forward_demodulation,[],[f433,f291]) ).
fof(f433,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),or(X2,possibly(and(not(X0),not(X1)))))),
inference(superposition,[],[f309,f222]) ).
fof(f437,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),or(X2,possibly(and(X0,not(X1)))))),
inference(forward_demodulation,[],[f432,f218]) ).
fof(f432,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),or(X2,possibly(and(X0,not(X1)))))),
inference(superposition,[],[f309,f219]) ).
fof(f424,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X1)),or(X0,possibly(X1)))),
inference(superposition,[],[f305,f279]) ).
fof(f428,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),implies(X2,possibly(and(not(X0),not(X1)))))),
inference(forward_demodulation,[],[f422,f291]) ).
fof(f422,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),implies(X2,possibly(and(not(X0),not(X1)))))),
inference(superposition,[],[f305,f222]) ).
fof(f427,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),implies(X2,possibly(and(X0,not(X1)))))),
inference(forward_demodulation,[],[f421,f218]) ).
fof(f421,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),implies(X2,possibly(and(X0,not(X1)))))),
inference(superposition,[],[f305,f219]) ).
fof(f418,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,and(not(X0),not(X1))))),
inference(superposition,[],[f301,f279]) ).
fof(f417,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(not(X0),not(X1)),and(X2,or(X0,X1))))),
inference(superposition,[],[f301,f222]) ).
fof(f416,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(X0,not(X1)),and(X2,implies(X0,X1))))),
inference(superposition,[],[f301,f219]) ).
fof(f415,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(necessarily(not(X0)),and(X1,possibly(X0))))),
inference(superposition,[],[f301,f221]) ).
fof(f410,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f257,f220]) ).
fof(f409,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f256,f220]) ).
fof(f413,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_equiv(X1,X0)) ),
inference(resolution,[],[f406,f242]) ).
fof(f412,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[],[f405,f242]) ).
fof(f411,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,[],[f287,f220]) ).
fof(f408,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(f404,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(not(X0),not(X1)),and(X2,or(X0,X1))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f300,f222]) ).
fof(f403,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,not(X1)),and(X2,implies(X0,X1))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f300,f219]) ).
fof(f402,plain,
! [X0,X1] :
( is_a_theorem(or(necessarily(not(X0)),and(X1,possibly(X0))))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f300,f221]) ).
fof(f300,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f253,f279]) ).
fof(f399,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),implies(X2,and(or(X0,X1),X2)))),
inference(superposition,[],[f299,f222]) ).
fof(f398,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X2,and(implies(X0,X1),X2)))),
inference(superposition,[],[f299,f219]) ).
fof(f397,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),implies(X1,and(possibly(X0),X1)))),
inference(superposition,[],[f299,f221]) ).
fof(f395,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f296,f222]) ).
fof(f394,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,X1),X2),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f296,f219]) ).
fof(f393,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(possibly(X0),X1),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f296,f221]) ).
fof(f392,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(strict_implies(not(X0),X1)) ),
inference(resolution,[],[f296,f242]) ).
fof(f295,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f242,f279]) ).
fof(f385,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(or(X0,X1),X2),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f294,f222]) ).
fof(f384,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(implies(X0,X1),X2),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f294,f219]) ).
fof(f383,plain,
! [X0,X1] : is_a_theorem(implies(equiv(possibly(X0),X1),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f294,f221]) ).
fof(f381,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,or(X0,X1)),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f293,f222]) ).
fof(f380,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,implies(X0,X1)),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f293,f219]) ).
fof(f379,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X1,possibly(X0)),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f293,f221]) ).
fof(f377,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f225,f291]) ).
fof(f370,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(or(X0,X1)))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f343,f222]) ).
fof(f369,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,X1)))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f343,f219]) ).
fof(f368,plain,
! [X0,X1] :
( ~ is_a_theorem(not(possibly(X0)))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f343,f221]) ).
fof(f358,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[],[f356,f279]) ).
fof(f356,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),or(X0,X1)),or(X0,X1))),
inference(superposition,[],[f238,f279]) ).
fof(f341,plain,
! [X0,X1] :
( ~ is_a_theorem(not(X0))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f337,f242]) ).
fof(f342,plain,
~ is_a_theorem(not(possibly(sK0))),
inference(resolution,[],[f337,f268]) ).
fof(f340,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(not(X0),not(X1)),X2))
| ~ is_a_theorem(or(X2,or(X0,X1))) ),
inference(superposition,[],[f322,f222]) ).
fof(f339,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[],[f322,f219]) ).
fof(f338,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(or(X1,possibly(X0))) ),
inference(superposition,[],[f322,f221]) ).
fof(f329,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),not(X1))))) = possibly(necessarily(or(X0,X1))),
inference(superposition,[],[f245,f222]) ).
fof(f334,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,not(X1))))) = possibly(strict_implies(X0,X1)),
inference(forward_demodulation,[],[f328,f218]) ).
fof(f328,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,not(X1))))) = possibly(necessarily(implies(X0,X1))),
inference(superposition,[],[f245,f219]) ).
fof(f317,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),necessarily(possibly(or(X0,X1))))),
inference(superposition,[],[f304,f222]) ).
fof(f316,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),necessarily(possibly(implies(X0,X1))))),
inference(superposition,[],[f304,f219]) ).
fof(f314,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(or(X0,X1),X2))),
inference(superposition,[],[f303,f222]) ).
fof(f313,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(implies(X0,X1),X2))),
inference(superposition,[],[f303,f219]) ).
fof(f311,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X2,or(X0,X1)))),
inference(superposition,[],[f302,f222]) ).
fof(f310,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(X2,implies(X0,X1)))),
inference(superposition,[],[f302,f219]) ).
fof(f308,plain,
! [X0,X1] : is_a_theorem(or(X1,or(X0,not(X1)))),
inference(superposition,[],[f298,f279]) ).
fof(f307,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),implies(X2,or(X0,X1)))),
inference(superposition,[],[f298,f222]) ).
fof(f306,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X2,implies(X0,X1)))),
inference(superposition,[],[f298,f219]) ).
fof(f290,plain,
! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(superposition,[],[f279,f222]) ).
fof(f289,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f279,f219]) ).
fof(f288,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(superposition,[],[f279,f221]) ).
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(f286,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f248,f242]) ).
fof(f282,plain,
! [X0,X1] : possibly(and(not(X0),not(X1))) = not(necessarily(or(X0,X1))),
inference(superposition,[],[f221,f222]) ).
fof(f280,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f219,f222]) ).
fof(f271,plain,
~ is_a_theorem(possibly(sK0)),
inference(resolution,[],[f269,f228]) ).
fof(f270,plain,
~ is_a_theorem(sK0),
inference(resolution,[],[f269,f249]) ).
fof(f269,plain,
~ is_a_theorem(necessarily(possibly(sK0))),
inference(resolution,[],[f268,f252]) ).
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(f98473,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98330]) ).
fof(f98330,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11849]) ).
fof(f11849,plain,
! [X0] : is_a_theorem(possibly(implies(X0,X0))),
inference(resolution,[],[f10236,f235]) ).
fof(f10236,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f9803,f6769]) ).
fof(f6769,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(possibly(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f6063,f242]) ).
fof(f6063,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,possibly(X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f6035,f1689]) ).
fof(f98472,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98342]) ).
fof(f98342,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11857]) ).
fof(f11857,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,equiv(X1,X1)))),
inference(resolution,[],[f10236,f231]) ).
fof(f98471,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98344]) ).
fof(f98344,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11858]) ).
fof(f11858,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,and(equiv(X1,X1),X0)))),
inference(resolution,[],[f10236,f234]) ).
fof(f98470,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98345]) ).
fof(f98345,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12191]) ).
fof(f12191,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,and(strict_equiv(X1,X1),X0)))),
inference(resolution,[],[f10259,f234]) ).
fof(f10259,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(strict_equiv(X1,X1),X0))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f9815,f6769]) ).
fof(f98469,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98346]) ).
fof(f98346,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12190]) ).
fof(f12190,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,strict_equiv(X1,X1)))),
inference(resolution,[],[f10259,f231]) ).
fof(f98468,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98348]) ).
fof(f98348,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24849]) ).
fof(f24849,plain,
( ! [X0,X1] : is_a_theorem(possibly(implies(necessarily(not(equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20954,f10236]) ).
fof(f98467,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98349]) ).
fof(f98349,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f24853]) ).
fof(f24853,plain,
( ! [X0,X1] : is_a_theorem(possibly(implies(necessarily(not(strict_equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20954,f10259]) ).
fof(f98466,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98351]) ).
fof(f98351,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f7073]) ).
fof(f7073,plain,
! [X0] : is_a_theorem(possibly(equiv(X0,X0))),
inference(subsumption_resolution,[],[f7011,f701]) ).
fof(f7011,plain,
! [X0] :
( is_a_theorem(possibly(equiv(X0,X0)))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f6769,f705]) ).
fof(f98465,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98355]) ).
fof(f98355,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18112]) ).
fof(f18112,plain,
( ! [X0] : is_a_theorem(possibly(not(not(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f10236]) ).
fof(f98464,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98356]) ).
fof(f98356,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f18116]) ).
fof(f18116,plain,
( ! [X0] : is_a_theorem(possibly(not(not(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18093,f10259]) ).
fof(f98463,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98358]) ).
fof(f98358,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23161]) ).
fof(f23161,plain,
( ! [X0,X1] : is_a_theorem(possibly(not(and(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19254,f10236]) ).
fof(f98462,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98359]) ).
fof(f98359,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23165]) ).
fof(f23165,plain,
( ! [X0,X1] : is_a_theorem(possibly(not(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19254,f10259]) ).
fof(f98461,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98361]) ).
fof(f98361,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23648]) ).
fof(f23648,plain,
( ! [X0] : is_a_theorem(possibly(not(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20187,f10236]) ).
fof(f98460,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98362]) ).
fof(f98362,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f23652]) ).
fof(f23652,plain,
( ! [X0] : is_a_theorem(possibly(not(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20187,f10259]) ).
fof(f98459,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98371]) ).
fof(f98371,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11863]) ).
fof(f11863,plain,
! [X0] : is_a_theorem(possibly(and(equiv(X0,X0),equiv(X0,X0)))),
inference(resolution,[],[f10236,f702]) ).
fof(f98458,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98372]) ).
fof(f98372,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11866]) ).
fof(f11866,plain,
! [X0,X1] : is_a_theorem(possibly(and(equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10236,f10385]) ).
fof(f98457,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98374]) ).
fof(f98374,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12199]) ).
fof(f12199,plain,
! [X0,X1] : is_a_theorem(possibly(and(equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10259,f10385]) ).
fof(f98456,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98375]) ).
fof(f98375,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12196]) ).
fof(f12196,plain,
! [X0] : is_a_theorem(possibly(and(strict_equiv(X0,X0),strict_equiv(X0,X0)))),
inference(resolution,[],[f10259,f702]) ).
fof(f98455,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98376]) ).
fof(f98376,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12200]) ).
fof(f12200,plain,
! [X0,X1] : is_a_theorem(possibly(and(strict_equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10259,f10689]) ).
fof(f98454,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98378]) ).
fof(f98378,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11867]) ).
fof(f11867,plain,
! [X0,X1] : is_a_theorem(possibly(and(strict_equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10236,f10689]) ).
fof(f98453,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98386]) ).
fof(f98386,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11872]) ).
fof(f11872,plain,
! [X0,X1] : is_a_theorem(possibly(or(X0,equiv(X1,X1)))),
inference(resolution,[],[f10236,f229]) ).
fof(f98452,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98387]) ).
fof(f98387,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11851]) ).
fof(f11851,plain,
! [X0] : is_a_theorem(possibly(or(X0,not(X0)))),
inference(resolution,[],[f10236,f293]) ).
fof(f98451,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98389]) ).
fof(f98389,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12205]) ).
fof(f12205,plain,
! [X0,X1] : is_a_theorem(possibly(or(X0,strict_equiv(X1,X1)))),
inference(resolution,[],[f10259,f229]) ).
fof(f98450,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98390]) ).
fof(f98390,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11878]) ).
fof(f11878,plain,
! [X0,X1] : is_a_theorem(possibly(or(equiv(X0,X0),X1))),
inference(resolution,[],[f10236,f230]) ).
fof(f98449,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98391]) ).
fof(f98391,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12211]) ).
fof(f12211,plain,
! [X0,X1] : is_a_theorem(possibly(or(strict_equiv(X0,X0),X1))),
inference(resolution,[],[f10259,f230]) ).
fof(f98448,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98395]) ).
fof(f98395,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11879]) ).
fof(f11879,plain,
! [X0] : is_a_theorem(possibly(necessarily(possibly(equiv(X0,X0))))),
inference(resolution,[],[f10236,f226]) ).
fof(f98447,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98396]) ).
fof(f98396,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12212]) ).
fof(f12212,plain,
! [X0] : is_a_theorem(possibly(necessarily(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f10259,f226]) ).
fof(f98446,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98403]) ).
fof(f98403,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12184]) ).
fof(f12184,plain,
! [X0] : is_a_theorem(possibly(strict_implies(X0,X0))),
inference(resolution,[],[f10259,f405]) ).
fof(f98445,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98405]) ).
fof(f98405,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45617]) ).
fof(f45617,plain,
( ! [X0,X1] : is_a_theorem(possibly(strict_implies(not(equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f41532,f18500]) ).
fof(f18500,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(possibly(X0)) )
| ~ spl1_3 ),
inference(resolution,[],[f18403,f2939]) ).
fof(f98444,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98406]) ).
fof(f98406,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f45647]) ).
fof(f45647,plain,
( ! [X0,X1] : is_a_theorem(possibly(strict_implies(not(strict_equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f41560,f18500]) ).
fof(f98443,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98407]) ).
fof(f98407,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f7077]) ).
fof(f7077,plain,
! [X0] : is_a_theorem(possibly(strict_equiv(X0,X0))),
inference(subsumption_resolution,[],[f7057,f1888]) ).
fof(f7057,plain,
! [X0] :
( is_a_theorem(possibly(strict_equiv(X0,X0)))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(resolution,[],[f6769,f727]) ).
fof(f98442,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98412]) ).
fof(f98412,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f92661]) ).
fof(f92661,plain,
( ! [X0] : is_a_theorem(possibly(possibly(implies(X0,X0))))
| ~ spl1_3 ),
inference(resolution,[],[f92627,f20775]) ).
fof(f20775,plain,
( ! [X0] :
( ~ is_a_theorem(or(possibly(X0),X0))
| is_a_theorem(possibly(possibly(X0))) )
| ~ spl1_3 ),
inference(resolution,[],[f18418,f6780]) ).
fof(f6780,plain,
! [X0,X1] :
( is_a_theorem(or(X0,possibly(X1)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f6779,f279]) ).
fof(f6779,plain,
! [X0,X1] :
( is_a_theorem(or(X0,possibly(X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f6063,f279]) ).
fof(f18418,plain,
( ! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(possibly(X0)) )
| ~ spl1_3 ),
inference(resolution,[],[f18408,f2156]) ).
fof(f98441,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98413]) ).
fof(f98413,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f11715]) ).
fof(f11715,plain,
! [X0] : is_a_theorem(possibly(possibly(equiv(X0,X0)))),
inference(resolution,[],[f11687,f7052]) ).
fof(f7052,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f6769,f6052]) ).
fof(f98440,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98415]) ).
fof(f98415,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f33798]) ).
fof(f33798,plain,
( ! [X0] : is_a_theorem(possibly(possibly(not(not(equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f20775,f27593]) ).
fof(f98439,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98416]) ).
fof(f98416,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f33799]) ).
fof(f33799,plain,
( ! [X0] : is_a_theorem(possibly(possibly(not(not(strict_equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f20775,f28263]) ).
fof(f98438,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98421]) ).
fof(f98421,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f93885]) ).
fof(f93885,plain,
( ! [X0] : is_a_theorem(possibly(possibly(or(X0,not(X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f93788,f20775]) ).
fof(f98437,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98426]) ).
fof(f98426,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f47184]) ).
fof(f47184,plain,
( ! [X0,X1] : is_a_theorem(possibly(possibly(strict_implies(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f45618,f20775]) ).
fof(f98436,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98427]) ).
fof(f98427,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f47828]) ).
fof(f47828,plain,
( ! [X0,X1] : is_a_theorem(possibly(possibly(strict_implies(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f45648,f20775]) ).
fof(f98435,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98428]) ).
fof(f98428,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18096,f12097]) ).
fof(f12097,plain,
! [X0] : is_a_theorem(possibly(possibly(strict_equiv(X0,X0)))),
inference(resolution,[],[f12072,f7052]) ).
fof(f98434,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98431]) ).
fof(f98431,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f33814]) ).
fof(f33814,plain,
( ! [X0] : is_a_theorem(possibly(possibly(possibly(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f20775,f11716]) ).
fof(f98433,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98432]) ).
fof(f98432,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18096,f33815]) ).
fof(f33815,plain,
( ! [X0] : is_a_theorem(possibly(possibly(possibly(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f20775,f12098]) ).
fof(f97475,plain,
( spl1_4
| spl1_5 ),
inference(avatar_split_clause,[],[f92597,f97473,f18095]) ).
fof(f97473,plain,
( spl1_5
<=> ! [X0] : is_a_theorem(necessarily(possibly(implies(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f92597,plain,
! [X0,X1] :
( is_a_theorem(necessarily(possibly(implies(X0,X0))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f92490,f8182]) ).
fof(f8182,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(possibly(X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5910,f242]) ).
fof(f5910,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,necessarily(possibly(X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f226]) ).
fof(f18097,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f18040,f18095,f18092]) ).
fof(f18040,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,not(not(X1)))) ),
inference(resolution,[],[f11324,f5929]) ).
fof(f11324,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,and(X1,not(not(X0)))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1299,f5767]) ).
fof(f350,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f341,f348,f345]) ).
fof(f345,plain,
( spl1_1
<=> ! [X1] : is_a_theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f348,plain,
( spl1_2
<=> ! [X0] :
( ~ is_a_theorem(not(X0))
| ~ is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : LCL549+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 23:16:32 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (31920)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.38 % (31923)WARNING: value z3 for option sas not known
% 0.19/0.38 % (31924)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.38 % (31925)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)
% 0.19/0.38 % (31927)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)
% 0.19/0.38 % (31922)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.38 % (31923)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)
% 0.19/0.38 % (31926)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)
% 0.19/0.38 % (31921)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.38 TRYING [1]
% 0.19/0.39 TRYING [2]
% 0.19/0.39 TRYING [3]
% 0.19/0.39 TRYING [1]
% 0.19/0.40 TRYING [2]
% 0.19/0.41 TRYING [4]
% 0.19/0.42 TRYING [3]
% 0.19/0.47 TRYING [4]
% 0.19/0.47 TRYING [5]
% 1.37/0.60 TRYING [1]
% 1.37/0.60 TRYING [2]
% 1.37/0.60 TRYING [3]
% 1.37/0.62 TRYING [4]
% 1.93/0.67 TRYING [5]
% 2.28/0.69 TRYING [5]
% 2.72/0.75 TRYING [6]
% 4.35/1.00 TRYING [6]
% 12.68/2.18 TRYING [7]
% 12.68/2.21 TRYING [6]
% 16.82/2.79 TRYING [7]
% 58.39/8.73 TRYING [8]
% 77.91/11.58 TRYING [8]
% 108.75/15.94 % (31923)First to succeed.
% 108.75/15.97 % (31923)Refutation found. Thanks to Tanya!
% 108.75/15.97 % SZS status Theorem for theBenchmark
% 108.75/15.97 % SZS output start Proof for theBenchmark
% See solution above
% 108.75/15.98 % (31923)------------------------------
% 108.75/15.98 % (31923)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 108.75/15.98 % (31923)Termination reason: Refutation
% 108.75/15.98
% 108.75/15.98 % (31923)Memory used [KB]: 70395
% 108.75/15.98 % (31923)Time elapsed: 15.585 s
% 108.75/15.98 % (31923)Instructions burned: 53203 (million)
% 108.75/15.98 % (31923)------------------------------
% 108.75/15.98 % (31923)------------------------------
% 108.75/15.98 % (31920)Success in time 15.567 s
%------------------------------------------------------------------------------