TSTP Solution File: LCL548+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL548+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 00:29:15 EDT 2024
% Result : Theorem 133.67s 19.52s
% Output : Refutation 133.67s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f137539,plain,
$false,
inference(avatar_sat_refutation,[],[f348,f18096,f97476,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,f98974,f137342,f137344,f137346,f137348]) ).
fof(f137348,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f137347]) ).
fof(f137347,plain,
( $false
| ~ spl1_3 ),
inference(subsumption_resolution,[],[f137092,f1886]) ).
fof(f1886,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(resolution,[],[f1840,f714]) ).
fof(f714,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[],[f699,f278]) ).
fof(f278,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f222,f219]) ).
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_m9,
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
~ axiom_m9,
inference(flattening,[],[f90]) ).
fof(f90,negated_conjecture,
~ axiom_m9,
inference(negated_conjecture,[],[f89]) ).
fof(f89,conjecture,
axiom_m9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
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(f699,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f358,f231]) ).
fof(f231,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204]) ).
fof(f204,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f123]) ).
fof(f123,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_1) ).
fof(f230,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203]) ).
fof(f203,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_1) ).
fof(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(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(f224,plain,
~ is_a_theorem(strict_implies(possibly(possibly(sK0)),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_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f137,f159]) ).
fof(f159,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
=> ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0))) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
( axiom_m9
| ? [X0] : ~ is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
=> axiom_m9 ),
inference(unused_predicate_definition_removal,[],[f71]) ).
fof(f71,axiom,
( axiom_m9
<=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m9) ).
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(f358,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f238,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(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(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(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(f1840,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1066,f374]) ).
fof(f374,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f228,f289]) ).
fof(f289,plain,
! [X0,X1] : necessarily(or(X0,X1)) = strict_implies(not(X0),X1),
inference(superposition,[],[f218,f278]) ).
fof(f1066,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(forward_demodulation,[],[f1065,f218]) ).
fof(f1065,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(forward_demodulation,[],[f1026,f289]) ).
fof(f1026,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,not(X1))))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f917,f317]) ).
fof(f317,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(forward_demodulation,[],[f237,f278]) ).
fof(f917,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f790,f247]) ).
fof(f247,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f228,f218]) ).
fof(f790,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f553,f242]) ).
fof(f553,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f528,f242]) ).
fof(f528,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(necessarily(X0),necessarily(X1)))),
inference(forward_demodulation,[],[f239,f218]) ).
fof(f137092,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),possibly(sK0)))
| ~ spl1_3 ),
inference(superposition,[],[f224,f136276]) ).
fof(f136276,plain,
( ! [X0] : possibly(X0) = possibly(possibly(X0))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f136275,f221]) ).
fof(f136275,plain,
( ! [X0] : possibly(possibly(X0)) = not(necessarily(not(X0)))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f135949,f119225]) ).
fof(f119225,plain,
! [X0] : necessarily(X0) = necessarily(necessarily(X0)),
inference(subsumption_resolution,[],[f119032,f225]) ).
fof(f119032,plain,
! [X0] :
( ~ is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0)))
| necessarily(X0) = necessarily(necessarily(X0)) ),
inference(resolution,[],[f5573,f227]) ).
fof(f5573,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1))
| X0 = X1 ),
inference(resolution,[],[f1586,f241]) ).
fof(f1586,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f573,f242]) ).
fof(f573,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f240,f242]) ).
fof(f135949,plain,
( ! [X0] : possibly(possibly(X0)) = not(necessarily(necessarily(not(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f120768,f221]) ).
fof(f120768,plain,
( ! [X0] : possibly(not(X0)) = not(necessarily(X0))
| ~ spl1_3 ),
inference(superposition,[],[f221,f119154]) ).
fof(f119154,plain,
( ! [X0] : not(not(X0)) = X0
| ~ spl1_3 ),
inference(subsumption_resolution,[],[f119153,f18237]) ).
fof(f18237,plain,
( ! [X0] : is_a_theorem(or(not(X0),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18136,f853]) ).
fof(f853,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f324,f242]) ).
fof(f324,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(not(X0))),or(X0,X1))),
inference(superposition,[],[f317,f278]) ).
fof(f18136,plain,
( ! [X0] : is_a_theorem(or(X0,not(not(not(X0)))))
| ~ spl1_3 ),
inference(superposition,[],[f18092,f278]) ).
fof(f18092,plain,
( ! [X1] : is_a_theorem(implies(X1,not(not(X1))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f18091]) ).
fof(f18091,plain,
( spl1_3
<=> ! [X1] : is_a_theorem(implies(X1,not(not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f119153,plain,
( ! [X0] :
( ~ is_a_theorem(or(not(X0),X0))
| not(not(X0)) = X0 )
| ~ spl1_3 ),
inference(forward_demodulation,[],[f118779,f278]) ).
fof(f118779,plain,
( ! [X0] :
( ~ is_a_theorem(implies(not(not(X0)),X0))
| not(not(X0)) = X0 )
| ~ spl1_3 ),
inference(resolution,[],[f5573,f18092]) ).
fof(f137346,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f137345]) ).
fof(f137345,plain,
( $false
| ~ spl1_3 ),
inference(subsumption_resolution,[],[f137091,f699]) ).
fof(f137091,plain,
( ~ is_a_theorem(implies(possibly(sK0),possibly(sK0)))
| ~ spl1_3 ),
inference(superposition,[],[f268,f136276]) ).
fof(f268,plain,
~ is_a_theorem(implies(possibly(possibly(sK0)),possibly(sK0))),
inference(resolution,[],[f247,f224]) ).
fof(f137344,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f137343]) ).
fof(f137343,plain,
( $false
| ~ spl1_3 ),
inference(subsumption_resolution,[],[f137089,f737]) ).
fof(f737,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(subsumption_resolution,[],[f735,f699]) ).
fof(f735,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[],[f724,f223]) ).
fof(f724,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f700,f242]) ).
fof(f700,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f358,f234]) ).
fof(f137089,plain,
( ~ is_a_theorem(equiv(possibly(sK0),possibly(sK0)))
| ~ spl1_3 ),
inference(superposition,[],[f1365,f136276]) ).
fof(f1365,plain,
~ is_a_theorem(equiv(possibly(possibly(sK0)),possibly(sK0))),
inference(resolution,[],[f1240,f224]) ).
fof(f1240,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(forward_demodulation,[],[f1239,f218]) ).
fof(f1239,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1231,f223]) ).
fof(f1231,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1023,f228]) ).
fof(f1023,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f917,f232]) ).
fof(f137342,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f137341]) ).
fof(f137341,plain,
( $false
| ~ spl1_3 ),
inference(subsumption_resolution,[],[f137088,f737]) ).
fof(f137088,plain,
( ~ is_a_theorem(equiv(possibly(sK0),possibly(sK0)))
| ~ spl1_3 ),
inference(superposition,[],[f1371,f136276]) ).
fof(f1371,plain,
~ is_a_theorem(equiv(possibly(sK0),possibly(possibly(sK0)))),
inference(resolution,[],[f1251,f224]) ).
fof(f1251,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(forward_demodulation,[],[f1250,f218]) ).
fof(f1250,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(superposition,[],[f1242,f223]) ).
fof(f1242,plain,
! [X0,X1] :
( ~ is_a_theorem(and(X1,X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1024,f228]) ).
fof(f1024,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f917,f233]) ).
fof(f98974,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97477]) ).
fof(f97477,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f699]) ).
fof(f18095,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f18094]) ).
fof(f18094,plain,
( spl1_4
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f98973,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97481]) ).
fof(f97481,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f231]) ).
fof(f98972,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97482]) ).
fof(f97482,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92491]) ).
fof(f92491,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(resolution,[],[f10236,f235]) ).
fof(f10236,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(equiv(X2,X2),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f9803,f8116]) ).
fof(f8116,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5899,f242]) ).
fof(f5899,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,[],[f693,f242]) ).
fof(f693,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,[],[f693,f358]) ).
fof(f9789,plain,
! [X0,X1] : is_a_theorem(implies(X0,equiv(X1,X1))),
inference(subsumption_resolution,[],[f9683,f699]) ).
fof(f9683,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,equiv(X1,X1)))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(resolution,[],[f8116,f703]) ).
fof(f703,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f358,f240]) ).
fof(f98971,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97488]) ).
fof(f97488,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92501]) ).
fof(f92501,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,implies(X1,equiv(X2,X2)))),
inference(resolution,[],[f10236,f231]) ).
fof(f98970,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97489]) ).
fof(f97489,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f234]) ).
fof(f98969,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97491]) ).
fof(f97491,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20953]) ).
fof(f20953,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(necessarily(not(X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f320]) ).
fof(f320,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f317,f242]) ).
fof(f19284,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(X0),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19267,f6060]) ).
fof(f6060,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,necessarily(X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f6059,f278]) ).
fof(f6059,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,necessarily(X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5942,f278]) ).
fof(f5942,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f225]) ).
fof(f19267,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f219]) ).
fof(f18290,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18237,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,f278]) ).
fof(f8243,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5926,f278]) ).
fof(f5926,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f232]) ).
fof(f98968,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97492]) ).
fof(f97492,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24906]) ).
fof(f24906,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(necessarily(necessarily(not(X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20957,f320]) ).
fof(f20957,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(necessarily(X0)),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f6060]) ).
fof(f98967,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97493]) ).
fof(f97493,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23540]) ).
fof(f23540,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(and(X1,not(X0)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f19282,f320]) ).
fof(f19282,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,X1),X2),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19267,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,f278]) ).
fof(f8824,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(implies(not(X0),X2)) ),
inference(superposition,[],[f5927,f278]) ).
fof(f5927,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X2,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f233]) ).
fof(f98966,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97494]) ).
fof(f97494,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23560]) ).
fof(f23560,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,implies(and(not(X0),X1),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f19283,f320]) ).
fof(f19283,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,X1),X2),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19267,f8246]) ).
fof(f98965,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97495]) ).
fof(f97495,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9789]) ).
fof(f98964,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97498]) ).
fof(f97498,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18092]) ).
fof(f98963,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97501]) ).
fof(f97501,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28004]) ).
fof(f28004,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(not(equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f18618,f296]) ).
fof(f296,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(superposition,[],[f231,f278]) ).
fof(f18618,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(not(equiv(X1,X1)),X0))
| is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18112,f1643]) ).
fof(f1643,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f1592,f278]) ).
fof(f1592,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f999,f1252]) ).
fof(f1252,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1048,f372]) ).
fof(f372,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f258,f289]) ).
fof(f258,plain,
! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f242,f225]) ).
fof(f1048,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1011,f289]) ).
fof(f1011,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f917,f230]) ).
fof(f999,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f914,f242]) ).
fof(f914,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f756,f242]) ).
fof(f756,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(resolution,[],[f244,f358]) ).
fof(f244,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(global_subsumption,[],[f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f218,f192,f219,f193,f220,f194,f221,f195,f222,f196,f223,f197,f224,f198,f225,f199,f226,f200,f227,f201,f228,f202,f229,f203,f230,f204,f231,f205,f232,f206,f233,f207,f234,f208,f235,f209,f236,f210,f237,f211,f238,f212,f239,f213,f240,f214,f241,f215,f242,f216,f243,f217]) ).
fof(f217,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ or_3 ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',or_3) ).
fof(f18112,plain,
( ! [X0] : is_a_theorem(necessarily(not(not(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f10234]) ).
fof(f10234,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f9803,f5837]) ).
fof(f5837,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5789,f247]) ).
fof(f5789,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f5780,f218]) ).
fof(f5780,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f5765,f917]) ).
fof(f5765,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(f98962,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97502]) ).
fof(f97502,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28249]) ).
fof(f28249,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f19120,f296]) ).
fof(f19120,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(not(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18116,f1643]) ).
fof(f18116,plain,
( ! [X0] : is_a_theorem(necessarily(not(not(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f10257]) ).
fof(f10257,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(strict_equiv(X1,X1),X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f9815,f5837]) ).
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,f1886]) ).
fof(f9773,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,strict_equiv(X1,X1)))
| ~ is_a_theorem(strict_implies(X1,X1)) ),
inference(resolution,[],[f8116,f725]) ).
fof(f725,plain,
! [X0] : is_a_theorem(implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(superposition,[],[f700,f220]) ).
fof(f98961,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97503]) ).
fof(f97503,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19253]) ).
fof(f19253,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(not(X0),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f320]) ).
fof(f98960,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97504]) ).
fof(f97504,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23032]) ).
fof(f23032,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(X1,necessarily(not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f19162,f320]) ).
fof(f19162,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,necessarily(X1))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18289,f6060]) ).
fof(f18289,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,X1)),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18237,f8827]) ).
fof(f98959,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97505]) ).
fof(f97505,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23215]) ).
fof(f23215,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(and(necessarily(not(X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19257,f320]) ).
fof(f19257,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(necessarily(X0),X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f6060]) ).
fof(f98958,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97506]) ).
fof(f97506,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20186]) ).
fof(f20186,plain,
( ! [X0] : is_a_theorem(implies(X0,not(necessarily(necessarily(not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f320]) ).
fof(f18397,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(X0))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f6060]) ).
fof(f18291,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(X0)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18237,f6060]) ).
fof(f98957,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97507]) ).
fof(f97507,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23700]) ).
fof(f23700,plain,
( ! [X0] : is_a_theorem(implies(X0,not(necessarily(necessarily(necessarily(not(X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20190,f320]) ).
fof(f20190,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(necessarily(X0)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f6060]) ).
fof(f98956,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97508]) ).
fof(f97508,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f22641]) ).
fof(f22641,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(necessarily(and(X1,not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18395,f320]) ).
fof(f18395,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,X1))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f8827]) ).
fof(f98955,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97509]) ).
fof(f97509,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f22660]) ).
fof(f22660,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,not(necessarily(and(not(X0),X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f18396,f320]) ).
fof(f18396,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,X1))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f8246]) ).
fof(f98954,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97510]) ).
fof(f97510,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f700]) ).
fof(f98953,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97513]) ).
fof(f97513,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10384]) ).
fof(f10384,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,f999]) ).
fof(f9804,plain,
! [X0,X1] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[],[f9789,f278]) ).
fof(f98952,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97514]) ).
fof(f97514,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10688]) ).
fof(f10688,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,f999]) ).
fof(f9816,plain,
! [X0,X1] : is_a_theorem(or(X0,strict_equiv(X1,X1))),
inference(superposition,[],[f9791,f278]) ).
fof(f98951,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97516]) ).
fof(f97516,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f14429]) ).
fof(f14429,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(possibly(equiv(X1,X1)),X0))),
inference(resolution,[],[f11747,f234]) ).
fof(f11747,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f11715,f999]) ).
fof(f11715,plain,
! [X0,X1] : is_a_theorem(or(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f11686,f6441]) ).
fof(f6441,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f6060,f1168]) ).
fof(f1168,plain,
! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1044,f372]) ).
fof(f1044,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1005,f218]) ).
fof(f1005,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f917,f231]) ).
fof(f11686,plain,
! [X0] : is_a_theorem(necessarily(necessarily(possibly(equiv(X0,X0))))),
inference(resolution,[],[f10234,f226]) ).
fof(f98950,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97517]) ).
fof(f97517,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f14882]) ).
fof(f14882,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(possibly(strict_equiv(X1,X1)),X0))),
inference(resolution,[],[f12129,f234]) ).
fof(f12129,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f12097,f999]) ).
fof(f12097,plain,
! [X0,X1] : is_a_theorem(or(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12071,f6441]) ).
fof(f12071,plain,
! [X0] : is_a_theorem(necessarily(necessarily(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f10257,f226]) ).
fof(f98949,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97526]) ).
fof(f97526,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11960]) ).
fof(f11960,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),possibly(X0)))),
inference(forward_demodulation,[],[f11941,f221]) ).
fof(f11941,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),not(necessarily(not(X0)))))),
inference(resolution,[],[f10241,f1308]) ).
fof(f1308,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),not(X2)))
| is_a_theorem(implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f320,f283]) ).
fof(f283,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f273,f219]) ).
fof(f273,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f222,f219]) ).
fof(f10241,plain,
! [X0,X1] : is_a_theorem(implies(implies(equiv(X0,X0),necessarily(X1)),X1)),
inference(resolution,[],[f9803,f5942]) ).
fof(f98948,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97527]) ).
fof(f97527,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12269]) ).
fof(f12269,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(strict_equiv(X1,X1),possibly(X0)))),
inference(forward_demodulation,[],[f12250,f221]) ).
fof(f12250,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(strict_equiv(X1,X1),not(necessarily(not(X0)))))),
inference(resolution,[],[f10264,f1308]) ).
fof(f10264,plain,
! [X0,X1] : is_a_theorem(implies(implies(strict_equiv(X0,X0),necessarily(X1)),X1)),
inference(resolution,[],[f9815,f5942]) ).
fof(f98947,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97528]) ).
fof(f97528,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f229]) ).
fof(f98946,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97533]) ).
fof(f97533,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92546]) ).
fof(f92546,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(X1,equiv(X2,X2)))),
inference(resolution,[],[f10236,f229]) ).
fof(f98945,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97534]) ).
fof(f97534,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92493]) ).
fof(f92493,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,not(X1)))),
inference(resolution,[],[f10236,f291]) ).
fof(f291,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X1,not(X0)),or(X0,X1))),
inference(superposition,[],[f235,f278]) ).
fof(f98944,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97535]) ).
fof(f97535,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f299]) ).
fof(f299,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,and(X1,not(X0))))),
inference(superposition,[],[f234,f278]) ).
fof(f98943,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97536]) ).
fof(f97536,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f230]) ).
fof(f98942,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97537]) ).
fof(f97537,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92552]) ).
fof(f92552,plain,
! [X2,X0,X1] : is_a_theorem(implies(X0,or(equiv(X1,X1),X2))),
inference(resolution,[],[f10236,f230]) ).
fof(f98941,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97538]) ).
fof(f97538,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f226]) ).
fof(f98940,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97542]) ).
fof(f97542,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92553]) ).
fof(f92553,plain,
! [X0,X1] : is_a_theorem(implies(X0,necessarily(possibly(equiv(X1,X1))))),
inference(resolution,[],[f10236,f226]) ).
fof(f98939,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97546]) ).
fof(f97546,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45616]) ).
fof(f45616,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41533,f3748]) ).
fof(f3748,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1651,f1859]) ).
fof(f1859,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f1843,f228]) ).
fof(f1843,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1066,f1044]) ).
fof(f1651,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1625,f289]) ).
fof(f1625,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(or(X1,not(X0)))) ),
inference(resolution,[],[f1592,f317]) ).
fof(f41533,plain,
( ! [X0,X1] : is_a_theorem(not(not(strict_implies(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(superposition,[],[f32255,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(f32255,plain,
( ! [X0,X1] : is_a_theorem(not(possibly(and(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f23103,f18153]) ).
fof(f18153,plain,
( ! [X0] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(not(possibly(X0))) )
| ~ spl1_3 ),
inference(superposition,[],[f18097,f221]) ).
fof(f18097,plain,
( ! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18092,f242]) ).
fof(f23103,plain,
( ! [X0,X1] : is_a_theorem(necessarily(not(and(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19252,f10244]) ).
fof(f10244,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(equiv(X0,X0),X1))
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f10230,f218]) ).
fof(f10230,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(equiv(X0,X0),X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f9803,f917]) ).
fof(f19252,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(not(X0),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f1840]) ).
fof(f98938,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97547]) ).
fof(f97547,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45646]) ).
fof(f45646,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41561,f3748]) ).
fof(f41561,plain,
( ! [X0,X1] : is_a_theorem(not(not(strict_implies(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(superposition,[],[f32360,f266]) ).
fof(f32360,plain,
( ! [X0,X1] : is_a_theorem(not(possibly(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f23111,f18153]) ).
fof(f23111,plain,
( ! [X0,X1] : is_a_theorem(necessarily(not(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19252,f10267]) ).
fof(f10267,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(strict_equiv(X0,X0),X1))
| is_a_theorem(necessarily(X1)) ),
inference(forward_demodulation,[],[f10253,f218]) ).
fof(f10253,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(strict_equiv(X0,X0),X1)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f9815,f917]) ).
fof(f98937,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97550]) ).
fof(f97550,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9791]) ).
fof(f98936,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97551]) ).
fof(f97551,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6033]) ).
fof(f6033,plain,
! [X0] : is_a_theorem(implies(X0,possibly(X0))),
inference(resolution,[],[f5942,f226]) ).
fof(f98935,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97555]) ).
fof(f97555,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11716]) ).
fof(f11716,plain,
! [X0,X1] : is_a_theorem(implies(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f11686,f6036]) ).
fof(f6036,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f5942,f1167]) ).
fof(f1167,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1044,f261]) ).
fof(f261,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f258,f218]) ).
fof(f98934,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97556]) ).
fof(f97556,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12098]) ).
fof(f12098,plain,
! [X0,X1] : is_a_theorem(implies(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12071,f6036]) ).
fof(f98933,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97565]) ).
fof(f97565,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f238]) ).
fof(f98932,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97566]) ).
fof(f97566,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f240]) ).
fof(f98931,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97567]) ).
fof(f97567,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f243]) ).
fof(f98930,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97568]) ).
fof(f97568,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f244]) ).
fof(f98929,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97572]) ).
fof(f97572,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f756]) ).
fof(f98928,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97574]) ).
fof(f97574,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f760]) ).
fof(f760,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,X1),implies(or(X0,X1),implies(or(X2,not(X0)),X1)))),
inference(superposition,[],[f244,f278]) ).
fof(f98927,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97576]) ).
fof(f97576,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f695]) ).
fof(f695,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,not(X0)),implies(or(X0,X1),implies(X2,X1)))),
inference(superposition,[],[f243,f278]) ).
fof(f98926,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97577]) ).
fof(f97577,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f575]) ).
fof(f575,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,not(X0)),implies(or(X0,X1),equiv(X1,not(X0))))),
inference(superposition,[],[f240,f278]) ).
fof(f98925,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97578]) ).
fof(f97578,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f703]) ).
fof(f98924,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97580]) ).
fof(f97580,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2712]) ).
fof(f2712,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,f280]) ).
fof(f280,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
inference(superposition,[],[f219,f222]) ).
fof(f98923,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97582]) ).
fof(f97582,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2775]) ).
fof(f2775,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,[],[f2774,f280]) ).
fof(f2774,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,[],[f2717,f278]) ).
fof(f2717,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,f280]) ).
fof(f98922,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97583]) ).
fof(f97583,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2059]) ).
fof(f2059,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,[],[f322,f283]) ).
fof(f322,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,X1)),implies(and(X0,not(X1)),X2))),
inference(superposition,[],[f317,f219]) ).
fof(f98921,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97584]) ).
fof(f97584,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1309]) ).
fof(f1309,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X2,and(X0,not(X1))))),
inference(superposition,[],[f317,f283]) ).
fof(f98920,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97585]) ).
fof(f97585,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3025]) ).
fof(f3025,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,[],[f323,f283]) ).
fof(f323,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,X1)),implies(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f317,f222]) ).
fof(f98919,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97586]) ).
fof(f97586,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1324]) ).
fof(f1324,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),possibly(X2)),implies(necessarily(not(X2)),and(X0,not(X1))))),
inference(superposition,[],[f321,f283]) ).
fof(f321,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,possibly(X0)),implies(necessarily(not(X0)),X1))),
inference(superposition,[],[f317,f221]) ).
fof(f98918,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97588]) ).
fof(f97588,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9803]) ).
fof(f98917,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97589]) ).
fof(f97589,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10241]) ).
fof(f98916,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97590]) ).
fof(f97590,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1291]) ).
fof(f1291,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,f283]) ).
fof(f98915,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97591]) ).
fof(f97591,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1926]) ).
fof(f1926,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,f284]) ).
fof(f284,plain,
! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(forward_demodulation,[],[f274,f219]) ).
fof(f274,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),X2) = not(and(or(X0,X1),not(X2))),
inference(superposition,[],[f222,f222]) ).
fof(f98914,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97593]) ).
fof(f97593,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2772]) ).
fof(f2772,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,[],[f2714,f278]) ).
fof(f2714,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,f280]) ).
fof(f98913,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97594]) ).
fof(f97594,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2811]) ).
fof(f2811,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,[],[f2810,f278]) ).
fof(f2810,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,[],[f2754,f283]) ).
fof(f2754,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,[],[f322,f280]) ).
fof(f98912,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97595]) ).
fof(f97595,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2792]) ).
fof(f2792,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X1,X2),not(X0)),not(and(X0,or(X1,X2))))),
inference(forward_demodulation,[],[f2791,f278]) ).
fof(f2791,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(not(X1),X2),not(X0)),not(and(X0,or(X1,X2))))),
inference(forward_demodulation,[],[f2725,f283]) ).
fof(f2725,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(and(not(X1),not(X2)),not(X0)),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f317,f280]) ).
fof(f98911,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97596]) ).
fof(f97596,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3050]) ).
fof(f3050,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,[],[f3026,f280]) ).
fof(f3026,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,[],[f323,f284]) ).
fof(f98910,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97597]) ).
fof(f97597,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2821]) ).
fof(f2821,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,[],[f2820,f278]) ).
fof(f2820,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,[],[f2761,f283]) ).
fof(f2761,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,[],[f321,f280]) ).
fof(f98909,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97600]) ).
fof(f97600,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f761]) ).
fof(f761,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,f282]) ).
fof(f282,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(forward_demodulation,[],[f272,f219]) ).
fof(f272,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = not(and(possibly(X0),not(X1))),
inference(superposition,[],[f222,f221]) ).
fof(f98908,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97602]) ).
fof(f97602,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9815]) ).
fof(f98907,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97603]) ).
fof(f97603,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10264]) ).
fof(f98906,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97604]) ).
fof(f97604,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2058]) ).
fof(f2058,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(possibly(X0),implies(X1,X2)),implies(and(X1,not(X2)),necessarily(not(X0))))),
inference(superposition,[],[f322,f282]) ).
fof(f98905,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97605]) ).
fof(f97605,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f636]) ).
fof(f636,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),not(X1)),implies(X1,necessarily(not(X0))))),
inference(superposition,[],[f317,f282]) ).
fof(f98904,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97606]) ).
fof(f97606,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3024]) ).
fof(f3024,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,[],[f323,f282]) ).
fof(f98903,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97607]) ).
fof(f97607,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f939]) ).
fof(f939,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),possibly(X1)),implies(necessarily(not(X1)),necessarily(not(X0))))),
inference(superposition,[],[f321,f282]) ).
fof(f98902,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97609]) ).
fof(f97609,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11772]) ).
fof(f11772,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(equiv(X0,X0)),X1),X1)),
inference(resolution,[],[f11716,f1685]) ).
fof(f98901,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97610]) ).
fof(f97610,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12154]) ).
fof(f12154,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(strict_equiv(X0,X0)),X1),X1)),
inference(resolution,[],[f12098,f1685]) ).
fof(f98900,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97611]) ).
fof(f97611,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f235]) ).
fof(f98899,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97612]) ).
fof(f97612,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f236]) ).
fof(f98898,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97613]) ).
fof(f97613,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f291]) ).
fof(f98897,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97614]) ).
fof(f97614,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2711]) ).
fof(f2711,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X0,and(not(X1),not(X2))),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f236,f280]) ).
fof(f98896,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97615]) ).
fof(f97615,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f292]) ).
fof(f292,plain,
! [X0,X1] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f236,f278]) ).
fof(f98895,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97616]) ).
fof(f97616,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2710]) ).
fof(f2710,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(and(not(X1),not(X2)),X0),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f235,f280]) ).
fof(f98894,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97617]) ).
fof(f97617,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f232]) ).
fof(f98893,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97618]) ).
fof(f97618,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f233]) ).
fof(f98892,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97621]) ).
fof(f97621,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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,[],[f5926,f233]) ).
fof(f98891,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97622]) ).
fof(f97622,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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,[],[f5927,f233]) ).
fof(f98890,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97625]) ).
fof(f97625,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1290]) ).
fof(f1290,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(X1)),implies(implies(X0,X1),X2))),
inference(superposition,[],[f230,f283]) ).
fof(f98889,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97626]) ).
fof(f97626,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f7804]) ).
fof(f7804,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(equiv(X0,X1)))),
inference(superposition,[],[f1290,f1713]) ).
fof(f1713,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(f98888,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97627]) ).
fof(f97627,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f7809]) ).
fof(f7809,plain,
! [X0,X1] : is_a_theorem(implies(and(X1,not(X0)),not(equiv(X0,X1)))),
inference(superposition,[],[f231,f1713]) ).
fof(f98887,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97628]) ).
fof(f97628,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6043]) ).
fof(f6043,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(strict_implies(X0,X1)))),
inference(resolution,[],[f5942,f581]) ).
fof(f581,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),necessarily(not(strict_implies(X0,X1))))),
inference(superposition,[],[f226,f266]) ).
fof(f98886,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97629]) ).
fof(f97629,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18128]) ).
fof(f18128,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(implies(X0,X1))))
| ~ spl1_3 ),
inference(superposition,[],[f18092,f219]) ).
fof(f98885,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97630]) ).
fof(f97630,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f581]) ).
fof(f98884,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97631]) ).
fof(f97631,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28206]) ).
fof(f28206,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(equiv(X1,X1))),X2))
| ~ spl1_3 ),
inference(resolution,[],[f18621,f19282]) ).
fof(f18621,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,not(equiv(X1,X1))))
| is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18112,f2936]) ).
fof(f2936,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X1)))
| is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f2920,f1432]) ).
fof(f1432,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1414,f242]) ).
fof(f1414,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1045,f261]) ).
fof(f1045,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,and(X0,X1)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1006,f218]) ).
fof(f1006,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(implies(X1,and(X0,X1)))) ),
inference(resolution,[],[f917,f234]) ).
fof(f2920,plain,
! [X0,X1] :
( ~ is_a_theorem(and(not(X1),or(X0,X1)))
| is_a_theorem(X0) ),
inference(resolution,[],[f2884,f242]) ).
fof(f2884,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),or(X1,X0)),X1)),
inference(resolution,[],[f2769,f320]) ).
fof(f2769,plain,
! [X0,X1] : is_a_theorem(or(X1,not(and(not(X0),or(X1,X0))))),
inference(forward_demodulation,[],[f2700,f278]) ).
fof(f2700,plain,
! [X0,X1] : is_a_theorem(implies(not(X1),not(and(not(X0),or(X1,X0))))),
inference(superposition,[],[f234,f280]) ).
fof(f98883,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97632]) ).
fof(f97632,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28455]) ).
fof(f28455,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(strict_equiv(X1,X1))),X2))
| ~ spl1_3 ),
inference(resolution,[],[f19123,f19282]) ).
fof(f19123,plain,
( ! [X0,X1] :
( ~ is_a_theorem(or(X0,not(strict_equiv(X1,X1))))
| is_a_theorem(X0) )
| ~ spl1_3 ),
inference(resolution,[],[f18116,f2936]) ).
fof(f98882,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97633]) ).
fof(f97633,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8216]) ).
fof(f98881,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97634]) ).
fof(f97634,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8307]) ).
fof(f8307,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(necessarily(X1),X2)),X1)),
inference(resolution,[],[f8216,f5942]) ).
fof(f98880,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97635]) ).
fof(f97635,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8487]) ).
fof(f8487,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(necessarily(necessarily(X1)),X2)),X1)),
inference(resolution,[],[f8307,f5942]) ).
fof(f98879,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97636]) ).
fof(f97636,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8784]) ).
fof(f98878,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97637]) ).
fof(f97637,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8304]) ).
fof(f8304,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(and(X1,X2),X3)),X1)),
inference(resolution,[],[f8216,f5926]) ).
fof(f98877,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97638]) ).
fof(f97638,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8786]) ).
fof(f8786,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(and(X1,X2),X3)),X2)),
inference(resolution,[],[f5927,f8216]) ).
fof(f98876,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97639]) ).
fof(f97639,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8927]) ).
fof(f8927,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(X1,and(X2,X3))),X3)),
inference(resolution,[],[f8784,f5927]) ).
fof(f98875,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97640]) ).
fof(f97640,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8928]) ).
fof(f8928,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(X1,and(X2,X3))),X2)),
inference(resolution,[],[f8784,f5926]) ).
fof(f98874,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97641]) ).
fof(f97641,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8931]) ).
fof(f8931,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,necessarily(X2))),X2)),
inference(resolution,[],[f8784,f5942]) ).
fof(f98873,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97642]) ).
fof(f97642,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9194]) ).
fof(f9194,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,necessarily(necessarily(X2)))),X2)),
inference(resolution,[],[f8931,f5942]) ).
fof(f98872,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97643]) ).
fof(f97643,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6042]) ).
fof(f6042,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(X1)),X1)),
inference(resolution,[],[f5942,f233]) ).
fof(f98871,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97644]) ).
fof(f97644,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f31855]) ).
fof(f31855,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(not(not(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f23031,f1651]) ).
fof(f23031,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(X1,necessarily(not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f19162,f1840]) ).
fof(f98870,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97645]) ).
fof(f97645,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8218]) ).
fof(f8218,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,X2))),X1)),
inference(resolution,[],[f5926,f6042]) ).
fof(f98869,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97646]) ).
fof(f97646,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8392]) ).
fof(f8392,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(necessarily(X1),X2))),X1)),
inference(resolution,[],[f8218,f5942]) ).
fof(f98868,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97647]) ).
fof(f97647,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6125]) ).
fof(f6125,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(X1))),X1)),
inference(resolution,[],[f6042,f5942]) ).
fof(f98867,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97648]) ).
fof(f97648,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6198]) ).
fof(f6198,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(necessarily(X1)))),X1)),
inference(resolution,[],[f6125,f5942]) ).
fof(f98866,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97649]) ).
fof(f97649,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50240]) ).
fof(f50240,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6070,f6125]) ).
fof(f6070,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(necessarily(X1))))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f6050,f1689]) ).
fof(f6050,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(X0)),X0)),
inference(resolution,[],[f5942,f225]) ).
fof(f98865,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97650]) ).
fof(f97650,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8219]) ).
fof(f8219,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(and(X1,X2)))),X1)),
inference(resolution,[],[f5926,f6125]) ).
fof(f98864,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97651]) ).
fof(f97651,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8788]) ).
fof(f8788,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,X2))),X2)),
inference(resolution,[],[f5927,f6042]) ).
fof(f98863,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97652]) ).
fof(f97652,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9019]) ).
fof(f9019,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,necessarily(X2)))),X2)),
inference(resolution,[],[f8788,f5942]) ).
fof(f98862,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97653]) ).
fof(f97653,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8789]) ).
fof(f8789,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(and(X1,X2)))),X2)),
inference(resolution,[],[f5927,f6125]) ).
fof(f98861,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97654]) ).
fof(f97654,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6126]) ).
fof(f6126,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,strict_implies(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f6042,f218]) ).
fof(f98860,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97655]) ).
fof(f97655,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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(f98859,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97656]) ).
fof(f97656,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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(f98858,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97657]) ).
fof(f97657,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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,[],[f5926,f232]) ).
fof(f98857,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97658]) ).
fof(f97658,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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,[],[f5927,f232]) ).
fof(f98856,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97659]) ).
fof(f97659,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2884]) ).
fof(f98855,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97660]) ).
fof(f97660,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6044]) ).
fof(f6044,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),or(necessarily(X1),X0)),X1)),
inference(resolution,[],[f5942,f2884]) ).
fof(f98854,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97663]) ).
fof(f97663,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1925]) ).
fof(f1925,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2))),
inference(superposition,[],[f230,f284]) ).
fof(f98853,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97664]) ).
fof(f97664,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2709]) ).
fof(f2709,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(not(X1),not(X2)),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f231,f280]) ).
fof(f98852,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97665]) ).
fof(f97665,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28207]) ).
fof(f28207,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(not(equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f18621,f19283]) ).
fof(f98851,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97666]) ).
fof(f97666,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23105]) ).
fof(f23105,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(not(X0)),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19252,f1651]) ).
fof(f98850,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97667]) ).
fof(f97667,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24540]) ).
fof(f24540,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(not(necessarily(X0))),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23105,f5942]) ).
fof(f98849,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97668]) ).
fof(f97668,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28456]) ).
fof(f28456,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(and(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f19123,f19283]) ).
fof(f98848,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97669]) ).
fof(f97669,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f39264]) ).
fof(f39264,plain,
( ! [X0,X1] : is_a_theorem(implies(and(not(possibly(X0)),X1),not(X0)))
| ~ spl1_3 ),
inference(superposition,[],[f24540,f221]) ).
fof(f98847,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97670]) ).
fof(f97670,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8215]) ).
fof(f98846,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97671]) ).
fof(f97671,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8290]) ).
fof(f8290,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(necessarily(X0),X1),X2),X0)),
inference(resolution,[],[f8215,f5942]) ).
fof(f98845,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97672]) ).
fof(f97672,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8472]) ).
fof(f8472,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(necessarily(necessarily(X0)),X1),X2),X0)),
inference(resolution,[],[f8290,f5942]) ).
fof(f98844,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97673]) ).
fof(f97673,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8783]) ).
fof(f98843,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97674]) ).
fof(f97674,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8913]) ).
fof(f8913,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,necessarily(X1)),X2),X1)),
inference(resolution,[],[f8783,f5942]) ).
fof(f98842,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97675]) ).
fof(f97675,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9178]) ).
fof(f9178,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,necessarily(necessarily(X1))),X2),X1)),
inference(resolution,[],[f8913,f5942]) ).
fof(f98841,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97676]) ).
fof(f97676,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8287]) ).
fof(f8287,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(and(X0,X1),X2),X3),X0)),
inference(resolution,[],[f8215,f5926]) ).
fof(f98840,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97677]) ).
fof(f97677,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8793]) ).
fof(f8793,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(and(X0,X1),X2),X3),X1)),
inference(resolution,[],[f5927,f8215]) ).
fof(f98839,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97678]) ).
fof(f97678,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8909]) ).
fof(f8909,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(X0,and(X1,X2)),X3),X2)),
inference(resolution,[],[f8783,f5927]) ).
fof(f98838,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97679]) ).
fof(f97679,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8910]) ).
fof(f8910,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(X0,and(X1,X2)),X3),X1)),
inference(resolution,[],[f8783,f5926]) ).
fof(f98837,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97680]) ).
fof(f97680,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6041]) ).
fof(f6041,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(X0),X1),X0)),
inference(resolution,[],[f5942,f232]) ).
fof(f98836,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97681]) ).
fof(f97681,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6114]) ).
fof(f6114,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(X0)),X1),X0)),
inference(resolution,[],[f6041,f5942]) ).
fof(f98835,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97682]) ).
fof(f97682,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6187]) ).
fof(f6187,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(necessarily(X0))),X1),X0)),
inference(resolution,[],[f6114,f5942]) ).
fof(f98834,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97683]) ).
fof(f97683,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50256]) ).
fof(f50256,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(necessarily(necessarily(X0)))),X1),X0)),
inference(resolution,[],[f6070,f6114]) ).
fof(f98833,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97684]) ).
fof(f97684,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f32575]) ).
fof(f32575,plain,
( ! [X0,X1] : is_a_theorem(implies(and(necessarily(not(not(X0))),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23214,f1651]) ).
fof(f23214,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(necessarily(not(X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19257,f1840]) ).
fof(f98832,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97685]) ).
fof(f97685,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8222]) ).
fof(f8222,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,X1)),X2),X0)),
inference(resolution,[],[f5926,f6041]) ).
fof(f98831,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97686]) ).
fof(f97686,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8409]) ).
fof(f8409,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(necessarily(X0),X1)),X2),X0)),
inference(resolution,[],[f8222,f5942]) ).
fof(f98830,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97687]) ).
fof(f97687,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8223]) ).
fof(f8223,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(and(X0,X1))),X2),X0)),
inference(resolution,[],[f5926,f6114]) ).
fof(f98829,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97688]) ).
fof(f97688,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8795]) ).
fof(f8795,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,X1)),X2),X1)),
inference(resolution,[],[f5927,f6041]) ).
fof(f98828,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97689]) ).
fof(f97689,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9037]) ).
fof(f9037,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,necessarily(X1))),X2),X1)),
inference(resolution,[],[f8795,f5942]) ).
fof(f98827,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97690]) ).
fof(f97690,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8796]) ).
fof(f8796,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(and(X0,X1))),X2),X1)),
inference(resolution,[],[f5927,f6114]) ).
fof(f98826,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97691]) ).
fof(f97691,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6115]) ).
fof(f6115,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(strict_implies(X0,X1),X2),implies(X0,X1))),
inference(superposition,[],[f6041,f218]) ).
fof(f98825,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97692]) ).
fof(f97692,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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(f98824,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97693]) ).
fof(f97693,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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(f98823,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97701]) ).
fof(f97701,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f697]) ).
fof(f697,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))),
inference(forward_demodulation,[],[f694,f278]) ).
fof(f694,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X0),X2)))),
inference(superposition,[],[f243,f278]) ).
fof(f98822,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97702]) ).
fof(f97702,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f574]) ).
fof(f574,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,not(X0)),equiv(not(X0),X1)))),
inference(superposition,[],[f240,f278]) ).
fof(f98821,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97703]) ).
fof(f97703,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f759]) ).
fof(f759,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X2,X1),implies(or(not(X0),X2),X1)))),
inference(superposition,[],[f244,f278]) ).
fof(f98820,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97707]) ).
fof(f97707,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f322]) ).
fof(f98819,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97708]) ).
fof(f97708,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f821]) ).
fof(f821,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,necessarily(not(X1)))),implies(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f317,f263]) ).
fof(f263,plain,
! [X0,X1] : implies(X1,necessarily(not(X0))) = not(and(X1,possibly(X0))),
inference(superposition,[],[f219,f221]) ).
fof(f98818,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97709]) ).
fof(f97709,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1741]) ).
fof(f1741,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,[],[f317,f264]) ).
fof(f98817,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97710]) ).
fof(f97710,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2064]) ).
fof(f2064,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,[],[f322,f263]) ).
fof(f98816,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97711]) ).
fof(f97711,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2066]) ).
fof(f2066,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,[],[f322,f264]) ).
fof(f98815,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97712]) ).
fof(f97712,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2065]) ).
fof(f2065,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,[],[f322,f275]) ).
fof(f275,plain,
! [X0,X1] : or(X1,necessarily(not(X0))) = not(and(not(X1),possibly(X0))),
inference(superposition,[],[f222,f221]) ).
fof(f98814,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97713]) ).
fof(f97713,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2445]) ).
fof(f2445,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,[],[f322,f276]) ).
fof(f276,plain,
! [X2,X0,X1] : or(X2,and(X0,not(X1))) = not(and(not(X2),implies(X0,X1))),
inference(superposition,[],[f222,f219]) ).
fof(f98813,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97714]) ).
fof(f97714,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f317]) ).
fof(f98812,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97715]) ).
fof(f97715,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f324]) ).
fof(f98811,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97716]) ).
fof(f97716,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f755]) ).
fof(f755,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),equiv(not(X0),not(X0)))),
inference(superposition,[],[f703,f278]) ).
fof(f98810,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97717]) ).
fof(f97717,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f361]) ).
fof(f361,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[],[f359,f278]) ).
fof(f359,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,implies(not(X0),X1)),implies(not(X0),X1))),
inference(superposition,[],[f238,f278]) ).
fof(f98809,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97718]) ).
fof(f97718,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f323]) ).
fof(f98808,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97719]) ).
fof(f97719,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1109]) ).
fof(f1109,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,necessarily(not(X1)))),implies(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f317,f275]) ).
fof(f98807,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97720]) ).
fof(f97720,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2442]) ).
fof(f2442,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,[],[f317,f276]) ).
fof(f98806,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97721]) ).
fof(f97721,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3036]) ).
fof(f3036,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,[],[f323,f222]) ).
fof(f98805,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97722]) ).
fof(f97722,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3037]) ).
fof(f3037,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,[],[f323,f263]) ).
fof(f98804,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97723]) ).
fof(f97723,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3038]) ).
fof(f3038,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,[],[f323,f275]) ).
fof(f98803,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97724]) ).
fof(f97724,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3039]) ).
fof(f3039,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,[],[f323,f264]) ).
fof(f98802,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97725]) ).
fof(f97725,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3030]) ).
fof(f3030,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,[],[f323,f263]) ).
fof(f98801,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97726]) ).
fof(f97726,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3032]) ).
fof(f3032,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,[],[f323,f264]) ).
fof(f98800,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97728]) ).
fof(f97728,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f321]) ).
fof(f98799,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97729]) ).
fof(f97729,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f952]) ).
fof(f952,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,[],[f943,f218]) ).
fof(f943,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,[],[f321,f263]) ).
fof(f98798,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97730]) ).
fof(f97730,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1791]) ).
fof(f1791,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,[],[f1743,f218]) ).
fof(f1743,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,[],[f321,f264]) ).
fof(f98797,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97731]) ).
fof(f97731,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f3398]) ).
fof(f3398,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,[],[f3307,f289]) ).
fof(f3307,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,[],[f321,f277]) ).
fof(f277,plain,
! [X2,X0,X1] : or(X2,and(not(X0),not(X1))) = not(and(not(X2),or(X0,X1))),
inference(superposition,[],[f222,f222]) ).
fof(f98796,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97733]) ).
fof(f97733,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28075]) ).
fof(f28075,plain,
( ! [X0,X1] : is_a_theorem(implies(or(not(equiv(X0,X0)),X1),X1))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f28056,f278]) ).
fof(f28056,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(not(equiv(X0,X0))),X1),X1))
| ~ spl1_3 ),
inference(resolution,[],[f28004,f1685]) ).
fof(f98795,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97734]) ).
fof(f97734,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28321]) ).
fof(f28321,plain,
( ! [X0,X1] : is_a_theorem(implies(or(not(strict_equiv(X0,X0)),X1),X1))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f28302,f278]) ).
fof(f28302,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(not(strict_equiv(X0,X0))),X1),X1))
| ~ spl1_3 ),
inference(resolution,[],[f28249,f1685]) ).
fof(f98794,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97735]) ).
fof(f97735,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f225]) ).
fof(f98793,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97740]) ).
fof(f97740,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f227]) ).
fof(f98792,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97743]) ).
fof(f97743,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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,[],[f5926,f225]) ).
fof(f98791,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97744]) ).
fof(f97744,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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,[],[f5927,f225]) ).
fof(f98790,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97745]) ).
fof(f97745,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8262]) ).
fof(f8262,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(not(X0),X1)),or(X0,X1))),
inference(superposition,[],[f8229,f463]) ).
fof(f463,plain,
! [X0,X1] : equiv(not(X0),X1) = and(or(X0,X1),implies(X1,not(X0))),
inference(superposition,[],[f223,f278]) ).
fof(f98789,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97746]) ).
fof(f97746,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8843]) ).
fof(f8843,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,not(X1))),or(X1,X0))),
inference(superposition,[],[f8803,f464]) ).
fof(f464,plain,
! [X0,X1] : equiv(X1,not(X0)) = and(implies(X1,not(X0)),or(X0,X1)),
inference(superposition,[],[f223,f278]) ).
fof(f98788,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97752]) ).
fof(f97752,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f623]) ).
fof(f623,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(not(X0)),implies(possibly(X0),X1))),
inference(superposition,[],[f230,f282]) ).
fof(f98787,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97753]) ).
fof(f97753,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6051]) ).
fof(f6051,plain,
! [X0] : is_a_theorem(implies(necessarily(not(X0)),not(necessarily(possibly(X0))))),
inference(resolution,[],[f5942,f330]) ).
fof(f330,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(f98786,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97754]) ).
fof(f97754,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18123]) ).
fof(f18123,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(X0)),not(possibly(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f18092,f221]) ).
fof(f98785,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97755]) ).
fof(f97755,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f330]) ).
fof(f98784,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97756]) ).
fof(f97756,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24791]) ).
fof(f24791,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f20952,f10245]) ).
fof(f10245,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f10231,f218]) ).
fof(f10231,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(equiv(X1,X1),X0))) ),
inference(resolution,[],[f9803,f1592]) ).
fof(f20952,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(necessarily(not(X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f1840]) ).
fof(f98783,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97757]) ).
fof(f97757,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f51012]) ).
fof(f51012,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(not(necessarily(X0)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f6399,f18239]) ).
fof(f18239,plain,
( ! [X0] : is_a_theorem(strict_implies(not(not(X0)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18136,f1840]) ).
fof(f6399,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,necessarily(X1)))
| is_a_theorem(implies(necessarily(X0),X1)) ),
inference(resolution,[],[f6049,f5942]) ).
fof(f6049,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f5942,f553]) ).
fof(f98782,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97758]) ).
fof(f97758,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f51083]) ).
fof(f51083,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(not(necessarily(necessarily(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f51012,f5942]) ).
fof(f98781,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97759]) ).
fof(f97759,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24797]) ).
fof(f24797,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(strict_equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f20952,f10268]) ).
fof(f10268,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(strict_equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f10254,f218]) ).
fof(f10254,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(strict_equiv(X1,X1),X0))) ),
inference(resolution,[],[f9815,f1592]) ).
fof(f98780,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97761]) ).
fof(f97761,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24799]) ).
fof(f24799,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(possibly(equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f20952,f14871]) ).
fof(f14871,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f14856,f218]) ).
fof(f14856,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(possibly(equiv(X1,X1)),X0))) ),
inference(resolution,[],[f11772,f1592]) ).
fof(f98779,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97762]) ).
fof(f97762,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24800]) ).
fof(f24800,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(not(possibly(strict_equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f20952,f14998]) ).
fof(f14998,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(strict_equiv(X1,X1)),X0))
| is_a_theorem(X0) ),
inference(forward_demodulation,[],[f14983,f218]) ).
fof(f14983,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(implies(possibly(strict_equiv(X1,X1)),X0))) ),
inference(resolution,[],[f12154,f1592]) ).
fof(f98778,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97763]) ).
fof(f97763,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f51010]) ).
fof(f51010,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(possibly(X0))),not(X0)))
| ~ spl1_3 ),
inference(resolution,[],[f6399,f18321]) ).
fof(f18321,plain,
( ! [X0] : is_a_theorem(strict_implies(not(possibly(X0)),necessarily(not(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f18239,f221]) ).
fof(f98777,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97764]) ).
fof(f97764,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8229]) ).
fof(f98776,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97765]) ).
fof(f97765,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8258]) ).
fof(f8258,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(X0),X1)),X0)),
inference(resolution,[],[f8229,f5942]) ).
fof(f98775,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97766]) ).
fof(f97766,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8341]) ).
fof(f8341,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(necessarily(X0)),X1)),X0)),
inference(resolution,[],[f8258,f5942]) ).
fof(f98774,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97767]) ).
fof(f97767,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50286]) ).
fof(f50286,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(necessarily(necessarily(X0))),X1)),X0)),
inference(resolution,[],[f6070,f8258]) ).
fof(f98773,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97768]) ).
fof(f97768,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f31719]) ).
fof(f31719,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(and(not(not(X0)),X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f22659,f1651]) ).
fof(f22659,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(necessarily(and(not(X0),X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f18396,f1840]) ).
fof(f98772,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97769]) ).
fof(f97769,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8255]) ).
fof(f8255,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,X1),X2)),X0)),
inference(resolution,[],[f8229,f5926]) ).
fof(f98771,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97770]) ).
fof(f97770,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8434]) ).
fof(f8434,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(necessarily(X0),X1),X2)),X0)),
inference(resolution,[],[f8255,f5942]) ).
fof(f98770,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97771]) ).
fof(f97771,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8338]) ).
fof(f8338,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(and(X0,X1)),X2)),X0)),
inference(resolution,[],[f8258,f5926]) ).
fof(f98769,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97772]) ).
fof(f97772,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8803]) ).
fof(f98768,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97773]) ).
fof(f97773,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f31540]) ).
fof(f31540,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,not(not(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f22640,f1651]) ).
fof(f22640,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(necessarily(and(X1,not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18395,f1840]) ).
fof(f98767,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97774]) ).
fof(f97774,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8837]) ).
fof(f8837,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,X2))),X1)),
inference(resolution,[],[f8803,f5926]) ).
fof(f98766,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97775]) ).
fof(f97775,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9139]) ).
fof(f9139,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(necessarily(X1),X2))),X1)),
inference(resolution,[],[f8837,f5942]) ).
fof(f98765,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97776]) ).
fof(f97776,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8840]) ).
fof(f8840,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(X1))),X1)),
inference(resolution,[],[f8803,f5942]) ).
fof(f98764,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97777]) ).
fof(f97777,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8967]) ).
fof(f8967,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(necessarily(X1)))),X1)),
inference(resolution,[],[f8840,f5942]) ).
fof(f98763,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97778]) ).
fof(f97778,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50293]) ).
fof(f50293,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6070,f8840]) ).
fof(f98762,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97779]) ).
fof(f97779,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8964]) ).
fof(f8964,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(and(X1,X2)))),X1)),
inference(resolution,[],[f8840,f5926]) ).
fof(f98761,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97780]) ).
fof(f97780,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8807]) ).
fof(f8807,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,X1),X2)),X1)),
inference(resolution,[],[f5927,f8229]) ).
fof(f98760,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97781]) ).
fof(f97781,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9095]) ).
fof(f9095,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,necessarily(X1)),X2)),X1)),
inference(resolution,[],[f8807,f5942]) ).
fof(f98759,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97782]) ).
fof(f97782,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8808]) ).
fof(f8808,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(and(X0,X1)),X2)),X1)),
inference(resolution,[],[f5927,f8258]) ).
fof(f98758,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97783]) ).
fof(f97783,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8836]) ).
fof(f8836,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,X2))),X2)),
inference(resolution,[],[f8803,f5927]) ).
fof(f98757,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97784]) ).
fof(f97784,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9121]) ).
fof(f9121,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,necessarily(X2)))),X2)),
inference(resolution,[],[f8836,f5942]) ).
fof(f98756,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97785]) ).
fof(f97785,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8963]) ).
fof(f8963,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(and(X1,X2)))),X2)),
inference(resolution,[],[f8840,f5927]) ).
fof(f98755,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97786]) ).
fof(f97786,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6050]) ).
fof(f98754,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97787]) ).
fof(f97787,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23594]) ).
fof(f23594,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(not(X0)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f20185,f1651]) ).
fof(f20185,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(necessarily(not(X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f1840]) ).
fof(f98753,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97788]) ).
fof(f97788,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24970]) ).
fof(f24970,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(not(necessarily(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23594,f5942]) ).
fof(f98752,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97789]) ).
fof(f97789,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8233]) ).
fof(f8233,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,X1))),X0)),
inference(resolution,[],[f5926,f6050]) ).
fof(f98751,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97790]) ).
fof(f97790,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8324]) ).
fof(f8324,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(necessarily(X0),X1))),X0)),
inference(resolution,[],[f8233,f5942]) ).
fof(f98750,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97791]) ).
fof(f97791,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50300]) ).
fof(f50300,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(necessarily(necessarily(X0)),X1))),X0)),
inference(resolution,[],[f6070,f8233]) ).
fof(f98749,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97792]) ).
fof(f97792,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8321]) ).
fof(f8321,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(and(X0,X1),X2))),X0)),
inference(resolution,[],[f8233,f5926]) ).
fof(f98748,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97793]) ).
fof(f97793,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6077]) ).
fof(f6077,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(X0))),X0)),
inference(resolution,[],[f6050,f5942]) ).
fof(f98747,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97794]) ).
fof(f97794,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f38266]) ).
fof(f38266,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(not(not(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23699,f1651]) ).
fof(f23699,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(necessarily(necessarily(not(X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20190,f1840]) ).
fof(f98746,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97795]) ).
fof(f97795,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8234]) ).
fof(f8234,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,X1)))),X0)),
inference(resolution,[],[f5926,f6077]) ).
fof(f98745,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97796]) ).
fof(f97796,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8511]) ).
fof(f8511,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(necessarily(X0),X1)))),X0)),
inference(resolution,[],[f8234,f5942]) ).
fof(f98744,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97797]) ).
fof(f97797,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6136]) ).
fof(f6136,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(X0)))),X0)),
inference(resolution,[],[f6077,f5942]) ).
fof(f98743,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97798]) ).
fof(f97798,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6232]) ).
fof(f6232,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(necessarily(X0))))),X0)),
inference(resolution,[],[f6136,f5942]) ).
fof(f98742,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97799]) ).
fof(f97799,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8235]) ).
fof(f8235,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(and(X0,X1))))),X0)),
inference(resolution,[],[f5926,f6136]) ).
fof(f98741,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97802]) ).
fof(f97802,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28205]) ).
fof(f28205,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(not(equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18621,f20957]) ).
fof(f98740,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97803]) ).
fof(f97803,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28454]) ).
fof(f28454,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(not(strict_equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19123,f20957]) ).
fof(f98739,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97804]) ).
fof(f97804,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8811]) ).
fof(f8811,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,X1))),X1)),
inference(resolution,[],[f5927,f6050]) ).
fof(f98738,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97805]) ).
fof(f97805,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8949]) ).
fof(f8949,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,necessarily(X1)))),X1)),
inference(resolution,[],[f8811,f5942]) ).
fof(f98737,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97806]) ).
fof(f97806,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50311]) ).
fof(f50311,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,necessarily(necessarily(X1))))),X1)),
inference(resolution,[],[f6070,f8811]) ).
fof(f98736,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97807]) ).
fof(f97807,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8946]) ).
fof(f8946,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,and(X1,X2)))),X1)),
inference(resolution,[],[f8811,f5926]) ).
fof(f98735,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97808]) ).
fof(f97808,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8816]) ).
fof(f8816,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(and(X0,X1),X2))),X1)),
inference(resolution,[],[f5927,f8233]) ).
fof(f98734,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97809]) ).
fof(f97809,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8812]) ).
fof(f8812,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,X1)))),X1)),
inference(resolution,[],[f5927,f6077]) ).
fof(f98733,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97810]) ).
fof(f97810,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9219]) ).
fof(f9219,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,necessarily(X1))))),X1)),
inference(resolution,[],[f8812,f5942]) ).
fof(f98732,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97811]) ).
fof(f97811,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8813]) ).
fof(f8813,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(and(X0,X1))))),X1)),
inference(resolution,[],[f5927,f6136]) ).
fof(f98731,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97812]) ).
fof(f97812,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8945]) ).
fof(f8945,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,and(X1,X2)))),X2)),
inference(resolution,[],[f8811,f5927]) ).
fof(f98730,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97813]) ).
fof(f97813,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6137]) ).
fof(f6137,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(strict_implies(X0,X1))),implies(X0,X1))),
inference(superposition,[],[f6077,f218]) ).
fof(f98729,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97814]) ).
fof(f97814,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8326]) ).
fof(f8326,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(equiv(X0,X1))),implies(X0,X1))),
inference(superposition,[],[f8233,f223]) ).
fof(f98728,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97815]) ).
fof(f97815,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8951]) ).
fof(f8951,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(equiv(X0,X1))),implies(X1,X0))),
inference(superposition,[],[f8811,f223]) ).
fof(f98727,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97816]) ).
fof(f97816,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f42736]) ).
fof(f42736,plain,
( ! [X0] : is_a_theorem(implies(necessarily(necessarily(not(possibly(X0)))),not(X0)))
| ~ spl1_3 ),
inference(superposition,[],[f24970,f221]) ).
fof(f98726,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97817]) ).
fof(f97817,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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(f98725,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97818]) ).
fof(f97818,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,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(f98724,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97819]) ).
fof(f97819,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6078]) ).
fof(f6078,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_implies(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f6050,f218]) ).
fof(f98723,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97820]) ).
fof(f97820,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6079]) ).
fof(f6079,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_implies(not(X0),X1)),or(X0,X1))),
inference(superposition,[],[f6050,f289]) ).
fof(f98722,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97821]) ).
fof(f97821,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8259]) ).
fof(f8259,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_equiv(X0,X1)),strict_implies(X0,X1))),
inference(superposition,[],[f8229,f220]) ).
fof(f98721,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97822]) ).
fof(f97822,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f8841]) ).
fof(f8841,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(strict_equiv(X0,X1)),strict_implies(X1,X0))),
inference(superposition,[],[f8803,f220]) ).
fof(f98720,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97824]) ).
fof(f97824,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f725]) ).
fof(f98719,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97825]) ).
fof(f97825,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f248]) ).
fof(f248,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f225,f218]) ).
fof(f98718,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97826]) ).
fof(f97826,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f528]) ).
fof(f98717,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97827]) ).
fof(f97827,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f410]) ).
fof(f410,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(f98716,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97828]) ).
fof(f97828,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f246]) ).
fof(f246,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),necessarily(strict_implies(X0,X1)))),
inference(superposition,[],[f227,f218]) ).
fof(f98715,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97831]) ).
fof(f97831,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f294]) ).
fof(f294,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f248,f278]) ).
fof(f98714,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97832]) ).
fof(f97832,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f554]) ).
fof(f554,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,X1),X2),implies(strict_implies(X0,X1),necessarily(X2)))),
inference(superposition,[],[f528,f218]) ).
fof(f98713,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97833]) ).
fof(f97833,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2190]) ).
fof(f2190,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),implies(strict_implies(not(X0),X1),necessarily(X2)))),
inference(superposition,[],[f554,f278]) ).
fof(f98712,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97834]) ).
fof(f97834,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2734]) ).
fof(f2734,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,[],[f554,f280]) ).
fof(f98711,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97835]) ).
fof(f97835,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f556]) ).
fof(f556,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,implies(X0,X1)),implies(necessarily(X2),strict_implies(X0,X1)))),
inference(superposition,[],[f528,f218]) ).
fof(f98710,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97836]) ).
fof(f97836,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2191]) ).
fof(f2191,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,[],[f554,f218]) ).
fof(f98709,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97837]) ).
fof(f97837,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2735]) ).
fof(f2735,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,[],[f556,f280]) ).
fof(f98708,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97838]) ).
fof(f97838,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2721]) ).
fof(f2721,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,f280]) ).
fof(f98707,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97839]) ).
fof(f97839,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2272]) ).
fof(f2272,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,or(X0,X1)),implies(necessarily(X2),strict_implies(not(X0),X1)))),
inference(superposition,[],[f556,f278]) ).
fof(f98706,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97840]) ).
fof(f97840,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f408]) ).
fof(f408,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X0,X1))),
inference(superposition,[],[f232,f220]) ).
fof(f98705,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97841]) ).
fof(f97841,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f409]) ).
fof(f409,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X1,X0))),
inference(superposition,[],[f233,f220]) ).
fof(f98704,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97842]) ).
fof(f97842,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50523]) ).
fof(f50523,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),implies(X0,X1))),
inference(superposition,[],[f6115,f220]) ).
fof(f98703,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97843]) ).
fof(f97843,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50768]) ).
fof(f50768,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),implies(X1,X0))),
inference(superposition,[],[f6126,f220]) ).
fof(f98702,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97844]) ).
fof(f97844,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50553]) ).
fof(f50553,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f50523,f278]) ).
fof(f98701,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97845]) ).
fof(f97845,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f50798]) ).
fof(f50798,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X1,not(X0)),or(X0,X1))),
inference(superposition,[],[f50768,f278]) ).
fof(f98700,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97847]) ).
fof(f97847,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f737]) ).
fof(f98699,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97858]) ).
fof(f97858,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92646]) ).
fof(f92646,plain,
( ! [X0] : is_a_theorem(not(not(implies(X0,X0))))
| ~ spl1_3 ),
inference(resolution,[],[f92628,f18353]) ).
fof(f18353,plain,
( ! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(not(not(X0))) )
| ~ spl1_3 ),
inference(resolution,[],[f18286,f2154]) ).
fof(f2154,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[],[f1834,f242]) ).
fof(f1834,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1058,f261]) ).
fof(f1058,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(or(X0,X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1057,f218]) ).
fof(f1057,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(implies(or(X0,X0),X1))) ),
inference(forward_demodulation,[],[f1017,f218]) ).
fof(f1017,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(or(X0,X0),X1))) ),
inference(resolution,[],[f917,f756]) ).
fof(f18286,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(not(X0))))
| ~ spl1_3 ),
inference(resolution,[],[f18237,f1840]) ).
fof(f92628,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[],[f92491,f278]) ).
fof(f98698,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97859]) ).
fof(f97859,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18114]) ).
fof(f18114,plain,
( ! [X0] : is_a_theorem(not(not(equiv(X0,X0))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f9818]) ).
fof(f98697,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97861]) ).
fof(f97861,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28011]) ).
fof(f28011,plain,
( ! [X0] : is_a_theorem(not(not(not(not(equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18618,f18136]) ).
fof(f98696,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97862]) ).
fof(f97862,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28256]) ).
fof(f28256,plain,
( ! [X0] : is_a_theorem(not(not(not(not(strict_equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f19120,f18136]) ).
fof(f98695,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97867]) ).
fof(f97867,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f93870]) ).
fof(f93870,plain,
( ! [X0] : is_a_theorem(not(not(or(X0,not(X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f93789,f18353]) ).
fof(f93789,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X1)))),
inference(superposition,[],[f92493,f278]) ).
fof(f98694,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97872]) ).
fof(f97872,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f41533]) ).
fof(f98693,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97873]) ).
fof(f97873,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f41561]) ).
fof(f98692,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97874]) ).
fof(f97874,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18118]) ).
fof(f18118,plain,
( ! [X0] : is_a_theorem(not(not(strict_equiv(X0,X0))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f9835]) ).
fof(f98691,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97877]) ).
fof(f97877,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18121]) ).
fof(f18121,plain,
( ! [X0] : is_a_theorem(not(not(possibly(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f11747]) ).
fof(f98690,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97878]) ).
fof(f97878,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18122]) ).
fof(f18122,plain,
( ! [X0] : is_a_theorem(not(not(possibly(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f12129]) ).
fof(f98689,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97883]) ).
fof(f97883,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2701]) ).
fof(f2701,plain,
! [X0] : is_a_theorem(not(and(not(X0),or(X0,X0)))),
inference(superposition,[],[f700,f280]) ).
fof(f98688,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97884]) ).
fof(f97884,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2705]) ).
fof(f2705,plain,
! [X0,X1] : is_a_theorem(not(and(and(not(X0),not(X1)),or(X0,X1)))),
inference(superposition,[],[f699,f280]) ).
fof(f98687,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97885]) ).
fof(f97885,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2752]) ).
fof(f2752,plain,
! [X2,X0,X1] : is_a_theorem(not(and(and(and(not(X0),not(X1)),X2),or(X0,X1)))),
inference(superposition,[],[f232,f280]) ).
fof(f98686,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97886]) ).
fof(f97886,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2753]) ).
fof(f2753,plain,
! [X2,X0,X1] : is_a_theorem(not(and(and(X0,and(not(X1),not(X2))),or(X1,X2)))),
inference(superposition,[],[f233,f280]) ).
fof(f98685,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97887]) ).
fof(f97887,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2760]) ).
fof(f2760,plain,
! [X0,X1] : is_a_theorem(not(and(necessarily(and(not(X0),not(X1))),or(X0,X1)))),
inference(superposition,[],[f225,f280]) ).
fof(f98684,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97894]) ).
fof(f97894,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23104]) ).
fof(f23104,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19252,f10245]) ).
fof(f98683,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97895]) ).
fof(f97895,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23112]) ).
fof(f23112,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(strict_equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19252,f10268]) ).
fof(f98682,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97897]) ).
fof(f97897,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23171]) ).
fof(f23171,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(possibly(equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f11747]) ).
fof(f98681,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97898]) ).
fof(f97898,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23172]) ).
fof(f23172,plain,
( ! [X0,X1] : is_a_theorem(not(and(not(possibly(strict_equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f12129]) ).
fof(f98680,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97901]) ).
fof(f97901,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28216]) ).
fof(f28216,plain,
( ! [X0,X1] : is_a_theorem(not(and(necessarily(not(equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f18621,f19257]) ).
fof(f98679,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97902]) ).
fof(f97902,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28466]) ).
fof(f28466,plain,
( ! [X0,X1] : is_a_theorem(not(and(necessarily(not(strict_equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19123,f19257]) ).
fof(f98678,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97905]) ).
fof(f97905,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28215]) ).
fof(f28215,plain,
( ! [X0,X1] : is_a_theorem(not(and(X0,necessarily(not(equiv(X1,X1))))))
| ~ spl1_3 ),
inference(resolution,[],[f18621,f19162]) ).
fof(f98677,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97906]) ).
fof(f97906,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28465]) ).
fof(f28465,plain,
( ! [X0,X1] : is_a_theorem(not(and(X0,necessarily(not(strict_equiv(X1,X1))))))
| ~ spl1_3 ),
inference(resolution,[],[f19123,f19162]) ).
fof(f98676,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97912]) ).
fof(f97912,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28220]) ).
fof(f28220,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18621,f18396]) ).
fof(f98675,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97913]) ).
fof(f97913,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28470]) ).
fof(f28470,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19123,f18396]) ).
fof(f98674,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97915]) ).
fof(f97915,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28221]) ).
fof(f28221,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(X0,not(equiv(X1,X1))))))
| ~ spl1_3 ),
inference(resolution,[],[f18621,f18395]) ).
fof(f98673,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97916]) ).
fof(f97916,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28471]) ).
fof(f28471,plain,
( ! [X0,X1] : is_a_theorem(not(necessarily(and(X0,not(strict_equiv(X1,X1))))))
| ~ spl1_3 ),
inference(resolution,[],[f19123,f18395]) ).
fof(f98672,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97921]) ).
fof(f97921,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23593]) ).
fof(f23593,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f20185,f10245]) ).
fof(f98671,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97922]) ).
fof(f97922,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23601]) ).
fof(f23601,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(strict_equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f20185,f10268]) ).
fof(f98670,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97924]) ).
fof(f97924,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23658]) ).
fof(f23658,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(possibly(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f11747]) ).
fof(f98669,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97925]) ).
fof(f97925,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23659]) ).
fof(f23659,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(not(possibly(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f12129]) ).
fof(f98668,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97928]) ).
fof(f97928,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28219]) ).
fof(f28219,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f18621,f20190]) ).
fof(f98667,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97929]) ).
fof(f97929,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28469]) ).
fof(f28469,plain,
( ! [X0] : is_a_theorem(not(necessarily(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f19123,f20190]) ).
fof(f98666,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97937]) ).
fof(f97937,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f21927]) ).
fof(f21927,plain,
( ! [X0] : is_a_theorem(not(possibly(not(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18153,f18112]) ).
fof(f98665,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97938]) ).
fof(f97938,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f21928]) ).
fof(f21928,plain,
( ! [X0] : is_a_theorem(not(possibly(not(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18153,f18116]) ).
fof(f98664,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97940]) ).
fof(f97940,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f32255]) ).
fof(f98663,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97941]) ).
fof(f97941,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f32360]) ).
fof(f98662,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97943]) ).
fof(f97943,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f36028]) ).
fof(f36028,plain,
( ! [X0] : is_a_theorem(not(possibly(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f23592,f18153]) ).
fof(f23592,plain,
( ! [X0] : is_a_theorem(necessarily(not(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20185,f10244]) ).
fof(f98661,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f97944]) ).
fof(f97944,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f36049]) ).
fof(f36049,plain,
( ! [X0] : is_a_theorem(not(possibly(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f23600,f18153]) ).
fof(f23600,plain,
( ! [X0] : is_a_theorem(necessarily(not(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20185,f10267]) ).
fof(f98660,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97964]) ).
fof(f97964,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9822]) ).
fof(f9822,plain,
! [X0] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f9804,f2657]) ).
fof(f2657,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(and(X0,X0)) ),
inference(resolution,[],[f2154,f2121]) ).
fof(f2121,plain,
! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(resolution,[],[f1826,f234]) ).
fof(f1826,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1050,f247]) ).
fof(f1050,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1049,f218]) ).
fof(f1049,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(forward_demodulation,[],[f1013,f218]) ).
fof(f1013,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,implies(X0,X1))))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f917,f238]) ).
fof(f98659,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97965]) ).
fof(f97965,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11200]) ).
fof(f11200,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),equiv(X1,X1))),
inference(resolution,[],[f10384,f9818]) ).
fof(f98658,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97966]) ).
fof(f97966,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11201]) ).
fof(f11201,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),strict_equiv(X1,X1))),
inference(resolution,[],[f10384,f9835]) ).
fof(f98657,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97968]) ).
fof(f97968,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12754]) ).
fof(f12754,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),possibly(equiv(X1,X1)))),
inference(resolution,[],[f11960,f9818]) ).
fof(f98656,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97969]) ).
fof(f97969,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12758]) ).
fof(f12758,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f11960,f9835]) ).
fof(f98655,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97978]) ).
fof(f97978,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11247]) ).
fof(f11247,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),equiv(X1,X1))),
inference(resolution,[],[f10688,f9818]) ).
fof(f98654,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97979]) ).
fof(f97979,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9839]) ).
fof(f9839,plain,
! [X0] : is_a_theorem(and(strict_equiv(X0,X0),strict_equiv(X0,X0))),
inference(resolution,[],[f9816,f2657]) ).
fof(f98653,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97980]) ).
fof(f97980,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11248]) ).
fof(f11248,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),strict_equiv(X1,X1))),
inference(resolution,[],[f10688,f9835]) ).
fof(f98652,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97982]) ).
fof(f97982,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12861]) ).
fof(f12861,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),possibly(equiv(X1,X1)))),
inference(resolution,[],[f12269,f9818]) ).
fof(f98651,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97983]) ).
fof(f97983,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12865]) ).
fof(f12865,plain,
! [X0,X1] : is_a_theorem(and(strict_equiv(X0,X0),possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f12269,f9835]) ).
fof(f98650,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97990]) ).
fof(f97990,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f15017]) ).
fof(f15017,plain,
! [X0,X1] : is_a_theorem(and(possibly(equiv(X0,X0)),equiv(X1,X1))),
inference(resolution,[],[f14429,f9818]) ).
fof(f98649,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97991]) ).
fof(f97991,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f15021]) ).
fof(f15021,plain,
! [X0,X1] : is_a_theorem(and(possibly(equiv(X0,X0)),strict_equiv(X1,X1))),
inference(resolution,[],[f14429,f9835]) ).
fof(f98648,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97993]) ).
fof(f97993,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f15061]) ).
fof(f15061,plain,
! [X0,X1] : is_a_theorem(and(possibly(strict_equiv(X0,X0)),equiv(X1,X1))),
inference(resolution,[],[f14882,f9818]) ).
fof(f98647,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97994]) ).
fof(f97994,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f15065]) ).
fof(f15065,plain,
! [X0,X1] : is_a_theorem(and(possibly(strict_equiv(X0,X0)),strict_equiv(X1,X1))),
inference(resolution,[],[f14882,f9835]) ).
fof(f98646,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f97999]) ).
fof(f97999,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92628]) ).
fof(f98645,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98005]) ).
fof(f98005,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f296]) ).
fof(f98644,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98006]) ).
fof(f98006,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f297]) ).
fof(f297,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,and(not(X0),X1)))),
inference(superposition,[],[f234,f278]) ).
fof(f98643,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98008]) ).
fof(f98008,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20954]) ).
fof(f20954,plain,
( ! [X0,X1] : is_a_theorem(or(X0,implies(necessarily(not(not(X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f853]) ).
fof(f98642,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98009]) ).
fof(f98009,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9804]) ).
fof(f98641,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98010]) ).
fof(f98010,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f714]) ).
fof(f98640,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98013]) ).
fof(f98013,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28021]) ).
fof(f28021,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(not(equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f18618,f300]) ).
fof(f300,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[],[f229,f278]) ).
fof(f98639,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98014]) ).
fof(f98014,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18136]) ).
fof(f98638,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98015]) ).
fof(f98015,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28267]) ).
fof(f28267,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f19120,f300]) ).
fof(f98637,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98016]) ).
fof(f98016,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2769]) ).
fof(f98636,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98017]) ).
fof(f98017,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19254]) ).
fof(f19254,plain,
( ! [X0,X1] : is_a_theorem(or(X0,not(and(not(not(X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f853]) ).
fof(f98635,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98018]) ).
fof(f98018,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20187]) ).
fof(f20187,plain,
( ! [X0] : is_a_theorem(or(X0,not(necessarily(necessarily(not(not(X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f853]) ).
fof(f98634,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98024]) ).
fof(f98024,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10396]) ).
fof(f10396,plain,
! [X0,X1] : is_a_theorem(or(X0,and(equiv(X1,X1),not(X0)))),
inference(resolution,[],[f9818,f299]) ).
fof(f98633,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98025]) ).
fof(f98025,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f727]) ).
fof(f727,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f700,f278]) ).
fof(f98632,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98026]) ).
fof(f98026,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10700]) ).
fof(f10700,plain,
! [X0,X1] : is_a_theorem(or(X0,and(strict_equiv(X1,X1),not(X0)))),
inference(resolution,[],[f9835,f299]) ).
fof(f98631,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98028]) ).
fof(f98028,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f300]) ).
fof(f98630,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98029]) ).
fof(f98029,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f93789]) ).
fof(f98629,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98030]) ).
fof(f98030,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f398]) ).
fof(f398,plain,
! [X0,X1] : is_a_theorem(or(X1,or(X0,and(not(X1),not(X0))))),
inference(superposition,[],[f297,f278]) ).
fof(f98628,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98035]) ).
fof(f98035,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f301]) ).
fof(f301,plain,
! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1))),
inference(superposition,[],[f230,f278]) ).
fof(f98627,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98036]) ).
fof(f98036,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f302]) ).
fof(f302,plain,
! [X0] : is_a_theorem(or(X0,necessarily(possibly(not(X0))))),
inference(superposition,[],[f226,f278]) ).
fof(f98626,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98043]) ).
fof(f98043,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45619]) ).
fof(f45619,plain,
( ! [X2,X0,X1] : is_a_theorem(or(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41533,f20641]) ).
fof(f20641,plain,
( ! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X1,X0)) )
| ~ spl1_3 ),
inference(resolution,[],[f19173,f2937]) ).
fof(f2937,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(X0) ),
inference(resolution,[],[f2920,f285]) ).
fof(f285,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(f19173,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18289,f222]) ).
fof(f98625,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98044]) ).
fof(f98044,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45649]) ).
fof(f45649,plain,
( ! [X2,X0,X1] : is_a_theorem(or(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41561,f20641]) ).
fof(f98624,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98047]) ).
fof(f98047,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f9816]) ).
fof(f98623,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98051]) ).
fof(f98051,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11715]) ).
fof(f98622,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98052]) ).
fof(f98052,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f6069]) ).
fof(f6069,plain,
! [X0] : is_a_theorem(or(X0,possibly(not(X0)))),
inference(superposition,[],[f6033,f278]) ).
fof(f98621,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98053]) ).
fof(f98053,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12097]) ).
fof(f98620,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98054]) ).
fof(f98054,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92645]) ).
fof(f92645,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X0),X1)),
inference(resolution,[],[f92628,f17181]) ).
fof(f17181,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f8184,f709]) ).
fof(f709,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f708,f278]) ).
fof(f708,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f706,f278]) ).
fof(f706,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f358,f278]) ).
fof(f8184,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f8180,f278]) ).
fof(f8180,plain,
! [X2,X0,X1] :
( is_a_theorem(or(X0,or(X1,X2)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f5907,f278]) ).
fof(f5907,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,or(X1,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f230]) ).
fof(f98619,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98055]) ).
fof(f98055,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19267]) ).
fof(f98618,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98060]) ).
fof(f98060,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19172]) ).
fof(f19172,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),not(X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18289,f219]) ).
fof(f98617,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98061]) ).
fof(f98061,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18138]) ).
fof(f18138,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1))))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f18110,f278]) ).
fof(f18110,plain,
( ! [X0,X1] : is_a_theorem(implies(not(implies(X0,X1)),and(X0,not(X1))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f1308]) ).
fof(f98616,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98062]) ).
fof(f98062,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19284]) ).
fof(f98615,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98063]) ).
fof(f98063,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20957]) ).
fof(f98614,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98064]) ).
fof(f98064,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24911]) ).
fof(f24911,plain,
( ! [X0,X1] : is_a_theorem(or(implies(necessarily(necessarily(necessarily(X0))),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f20957,f6060]) ).
fof(f98613,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98065]) ).
fof(f98065,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19282]) ).
fof(f98612,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98066]) ).
fof(f98066,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19283]) ).
fof(f98611,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98067]) ).
fof(f98067,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23545]) ).
fof(f23545,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(X0,necessarily(X1)),X2),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19282,f6060]) ).
fof(f98610,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98068]) ).
fof(f98068,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23565]) ).
fof(f23565,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(and(necessarily(X0),X1),X2),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19283,f6060]) ).
fof(f98609,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98069]) ).
fof(f98069,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20955]) ).
fof(f20955,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(necessarily(and(X0,X1)),X2),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f8827]) ).
fof(f98608,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98070]) ).
fof(f98070,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20956]) ).
fof(f20956,plain,
( ! [X2,X0,X1] : is_a_theorem(or(implies(necessarily(and(X0,X1)),X2),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19284,f8246]) ).
fof(f98607,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98072]) ).
fof(f98072,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19175]) ).
fof(f19175,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,necessarily(not(X1))),possibly(X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18289,f263]) ).
fof(f98606,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98073]) ).
fof(f98073,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10401]) ).
fof(f10401,plain,
! [X0,X1] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(resolution,[],[f9818,f230]) ).
fof(f98605,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98076]) ).
fof(f98076,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18237]) ).
fof(f98604,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98077]) ).
fof(f98077,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19165]) ).
fof(f19165,plain,
( ! [X0,X1] : is_a_theorem(or(not(equiv(X0,X1)),implies(X1,X0)))
| ~ spl1_3 ),
inference(superposition,[],[f18289,f223]) ).
fof(f98603,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98078]) ).
fof(f98078,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19260]) ).
fof(f19260,plain,
( ! [X0,X1] : is_a_theorem(or(not(equiv(X0,X1)),implies(X0,X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f223]) ).
fof(f98602,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98080]) ).
fof(f98080,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28027]) ).
fof(f28027,plain,
( ! [X0,X1] : is_a_theorem(or(not(not(equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18618,f301]) ).
fof(f98601,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98081]) ).
fof(f98081,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28273]) ).
fof(f28273,plain,
( ! [X0,X1] : is_a_theorem(or(not(not(strict_equiv(X0,X0))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19120,f301]) ).
fof(f98600,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98082]) ).
fof(f98082,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18289]) ).
fof(f98599,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98083]) ).
fof(f98083,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18290]) ).
fof(f98598,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98084]) ).
fof(f98084,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19162]) ).
fof(f98597,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98085]) ).
fof(f98085,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23037]) ).
fof(f23037,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(X0,necessarily(necessarily(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f19162,f6060]) ).
fof(f98596,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98086]) ).
fof(f98086,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19160]) ).
fof(f19160,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(X0,and(X1,X2))),X2))
| ~ spl1_3 ),
inference(resolution,[],[f18289,f8827]) ).
fof(f98595,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98087]) ).
fof(f98087,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19161]) ).
fof(f19161,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(X0,and(X1,X2))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18289,f8246]) ).
fof(f98594,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98088]) ).
fof(f98088,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19257]) ).
fof(f98593,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98089]) ).
fof(f98089,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23220]) ).
fof(f23220,plain,
( ! [X0,X1] : is_a_theorem(or(not(and(necessarily(necessarily(X0)),X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19257,f6060]) ).
fof(f98592,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98090]) ).
fof(f98090,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19255]) ).
fof(f19255,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(and(X0,X1),X2)),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f8827]) ).
fof(f98591,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98091]) ).
fof(f98091,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19256]) ).
fof(f19256,plain,
( ! [X2,X0,X1] : is_a_theorem(or(not(and(and(X0,X1),X2)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18290,f8246]) ).
fof(f98590,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98092]) ).
fof(f98092,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18291]) ).
fof(f98589,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98093]) ).
fof(f98093,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18397]) ).
fof(f98588,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98094]) ).
fof(f98094,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20190]) ).
fof(f98587,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98095]) ).
fof(f98095,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23705]) ).
fof(f23705,plain,
( ! [X0] : is_a_theorem(or(not(necessarily(necessarily(necessarily(necessarily(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f20190,f6060]) ).
fof(f98586,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98096]) ).
fof(f98096,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20189]) ).
fof(f20189,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(necessarily(and(X0,X1)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f8246]) ).
fof(f98585,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98097]) ).
fof(f98097,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18396]) ).
fof(f98584,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98098]) ).
fof(f98098,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f22665]) ).
fof(f22665,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(necessarily(X0),X1))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f18396,f6060]) ).
fof(f98583,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98099]) ).
fof(f98099,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18395]) ).
fof(f98582,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98100]) ).
fof(f98100,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f22646]) ).
fof(f22646,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(and(X0,necessarily(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18395,f6060]) ).
fof(f98581,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98101]) ).
fof(f98101,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20188]) ).
fof(f20188,plain,
( ! [X0,X1] : is_a_theorem(or(not(necessarily(necessarily(and(X0,X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f18397,f8827]) ).
fof(f98580,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98102]) ).
fof(f98102,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18399]) ).
fof(f18399,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_implies(X0,X1)),implies(X0,X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18291,f218]) ).
fof(f98579,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98103]) ).
fof(f98103,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19164]) ).
fof(f19164,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_equiv(X0,X1)),strict_implies(X1,X0)))
| ~ spl1_3 ),
inference(superposition,[],[f18289,f220]) ).
fof(f98578,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98104]) ).
fof(f98104,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19259]) ).
fof(f19259,plain,
( ! [X0,X1] : is_a_theorem(or(not(strict_equiv(X0,X1)),strict_implies(X0,X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f220]) ).
fof(f98577,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98108]) ).
fof(f98108,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f718]) ).
fof(f718,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X0,X1))),
inference(superposition,[],[f714,f219]) ).
fof(f98576,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98109]) ).
fof(f98109,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2773]) ).
fof(f2773,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,[],[f2716,f278]) ).
fof(f2716,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,f280]) ).
fof(f98575,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98110]) ).
fof(f98110,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2771]) ).
fof(f2771,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,[],[f2713,f278]) ).
fof(f2713,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,f280]) ).
fof(f98574,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98115]) ).
fof(f98115,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2781]) ).
fof(f2781,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,[],[f2780,f278]) ).
fof(f2780,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,[],[f2779,f280]) ).
fof(f2779,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,[],[f2778,f280]) ).
fof(f2778,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,[],[f2719,f278]) ).
fof(f2719,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,f280]) ).
fof(f98573,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98118]) ).
fof(f98118,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19173]) ).
fof(f98572,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98119]) ).
fof(f98119,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19268]) ).
fof(f19268,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0)))
| ~ spl1_3 ),
inference(superposition,[],[f18290,f222]) ).
fof(f98571,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98120]) ).
fof(f98120,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19176]) ).
fof(f19176,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,necessarily(not(X1))),possibly(X1)))
| ~ spl1_3 ),
inference(superposition,[],[f18289,f275]) ).
fof(f98570,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98121]) ).
fof(f98121,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f93869]) ).
fof(f93869,plain,
! [X0,X1] : is_a_theorem(or(or(X0,not(X0)),X1)),
inference(resolution,[],[f93789,f17181]) ).
fof(f98569,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98122]) ).
fof(f98122,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f303]) ).
fof(f303,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),implies(X1,possibly(X0)))),
inference(superposition,[],[f296,f221]) ).
fof(f98568,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98123]) ).
fof(f98123,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f307]) ).
fof(f307,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),or(X1,possibly(X0)))),
inference(superposition,[],[f300,f221]) ).
fof(f98567,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98124]) ).
fof(f98124,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f310]) ).
fof(f310,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),or(possibly(X0),X1))),
inference(superposition,[],[f301,f221]) ).
fof(f98566,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98125]) ).
fof(f98125,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f313]) ).
fof(f313,plain,
! [X0] : is_a_theorem(or(necessarily(not(X0)),necessarily(possibly(possibly(X0))))),
inference(superposition,[],[f302,f221]) ).
fof(f98565,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98130]) ).
fof(f98130,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45613]) ).
fof(f45613,plain,
( ! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f41533,f341]) ).
fof(f341,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f335,f278]) ).
fof(f335,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(resolution,[],[f320,f250]) ).
fof(f250,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f242,f229]) ).
fof(f98564,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98131]) ).
fof(f98131,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45643]) ).
fof(f45643,plain,
( ! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f41561,f341]) ).
fof(f98563,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98134]) ).
fof(f98134,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10705]) ).
fof(f10705,plain,
! [X0,X1] : is_a_theorem(or(strict_equiv(X0,X0),X1)),
inference(resolution,[],[f9835,f230]) ).
fof(f98562,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98137]) ).
fof(f98137,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f14451]) ).
fof(f14451,plain,
! [X0,X1] : is_a_theorem(or(possibly(equiv(X0,X0)),X1)),
inference(resolution,[],[f11747,f230]) ).
fof(f98561,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98138]) ).
fof(f98138,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f14904]) ).
fof(f14904,plain,
! [X0,X1] : is_a_theorem(or(possibly(strict_equiv(X0,X0)),X1)),
inference(resolution,[],[f12129,f230]) ).
fof(f98560,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98139]) ).
fof(f98139,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18402]) ).
fof(f18402,plain,
( ! [X0] : is_a_theorem(or(possibly(X0),not(X0)))
| ~ spl1_3 ),
inference(superposition,[],[f18291,f221]) ).
fof(f98559,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98140]) ).
fof(f98140,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18139]) ).
fof(f18139,plain,
( ! [X0] : is_a_theorem(or(possibly(X0),necessarily(not(X0))))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f18119,f278]) ).
fof(f18119,plain,
( ! [X0] : is_a_theorem(implies(not(possibly(X0)),necessarily(not(X0))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f635]) ).
fof(f635,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(X1)))
| is_a_theorem(implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f320,f282]) ).
fof(f98558,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98142]) ).
fof(f98142,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f5853]) ).
fof(f5853,plain,
! [X0] : is_a_theorem(necessarily(equiv(X0,X0))),
inference(subsumption_resolution,[],[f5846,f699]) ).
fof(f5846,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(resolution,[],[f5789,f2125]) ).
fof(f2125,plain,
! [X0] : is_a_theorem(strict_implies(implies(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f1826,f240]) ).
fof(f98557,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98147]) ).
fof(f98147,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18112]) ).
fof(f98556,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98148]) ).
fof(f98148,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18116]) ).
fof(f98555,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98150]) ).
fof(f98150,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23103]) ).
fof(f98554,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98151]) ).
fof(f98151,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23111]) ).
fof(f98553,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98154]) ).
fof(f98154,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23592]) ).
fof(f98552,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98155]) ).
fof(f98155,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23600]) ).
fof(f98551,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98167]) ).
fof(f98167,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11670]) ).
fof(f11670,plain,
! [X0] : is_a_theorem(necessarily(and(equiv(X0,X0),equiv(X0,X0)))),
inference(resolution,[],[f10234,f700]) ).
fof(f98550,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98168]) ).
fof(f98168,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11673]) ).
fof(f11673,plain,
! [X0,X1] : is_a_theorem(necessarily(and(equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10234,f10384]) ).
fof(f98549,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98170]) ).
fof(f98170,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12058]) ).
fof(f12058,plain,
! [X0,X1] : is_a_theorem(necessarily(and(equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10257,f10384]) ).
fof(f98548,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98171]) ).
fof(f98171,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12055]) ).
fof(f12055,plain,
! [X0] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),strict_equiv(X0,X0)))),
inference(resolution,[],[f10257,f700]) ).
fof(f98547,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98172]) ).
fof(f98172,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12059]) ).
fof(f12059,plain,
! [X0,X1] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10257,f10688]) ).
fof(f98546,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98174]) ).
fof(f98174,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11674]) ).
fof(f11674,plain,
! [X0,X1] : is_a_theorem(necessarily(and(strict_equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10234,f10688]) ).
fof(f98545,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98181]) ).
fof(f98181,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11686]) ).
fof(f98544,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98182]) ).
fof(f98182,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12071]) ).
fof(f98543,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98185]) ).
fof(f98185,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f5867]) ).
fof(f5867,plain,
! [X0] : is_a_theorem(necessarily(strict_implies(X0,X0))),
inference(resolution,[],[f5854,f1041]) ).
fof(f1041,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X1,X0))) ),
inference(resolution,[],[f917,f409]) ).
fof(f5854,plain,
! [X0] : is_a_theorem(necessarily(strict_equiv(X0,X0))),
inference(subsumption_resolution,[],[f5851,f1886]) ).
fof(f5851,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(necessarily(strict_equiv(X0,X0))) ),
inference(resolution,[],[f5789,f2130]) ).
fof(f2130,plain,
! [X0] : is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(resolution,[],[f1826,f410]) ).
fof(f98542,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98187]) ).
fof(f98187,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45617]) ).
fof(f45617,plain,
( ! [X0,X1] : is_a_theorem(necessarily(strict_implies(not(equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f41533,f18318]) ).
fof(f18318,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(necessarily(X0)) )
| ~ spl1_3 ),
inference(resolution,[],[f18239,f5789]) ).
fof(f98541,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98188]) ).
fof(f98188,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45647]) ).
fof(f45647,plain,
( ! [X0,X1] : is_a_theorem(necessarily(strict_implies(not(strict_equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f41561,f18318]) ).
fof(f98540,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98189]) ).
fof(f98189,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f5854]) ).
fof(f98539,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98199]) ).
fof(f98199,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10402]) ).
fof(f10402,plain,
! [X0] : is_a_theorem(necessarily(possibly(equiv(X0,X0)))),
inference(resolution,[],[f9818,f226]) ).
fof(f98538,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98202]) ).
fof(f98202,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28028]) ).
fof(f28028,plain,
( ! [X0] : is_a_theorem(necessarily(possibly(not(not(equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f18618,f302]) ).
fof(f98537,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98203]) ).
fof(f98203,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28274]) ).
fof(f28274,plain,
( ! [X0] : is_a_theorem(necessarily(possibly(not(not(strict_equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f19120,f302]) ).
fof(f98536,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98212]) ).
fof(f98212,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10706]) ).
fof(f10706,plain,
! [X0] : is_a_theorem(necessarily(possibly(strict_equiv(X0,X0)))),
inference(resolution,[],[f9835,f226]) ).
fof(f98535,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98215]) ).
fof(f98215,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f14452]) ).
fof(f14452,plain,
! [X0] : is_a_theorem(necessarily(possibly(possibly(equiv(X0,X0))))),
inference(resolution,[],[f11747,f226]) ).
fof(f98534,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98216]) ).
fof(f98216,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f14905]) ).
fof(f14905,plain,
! [X0] : is_a_theorem(necessarily(possibly(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f12129,f226]) ).
fof(f98533,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98217]) ).
fof(f98217,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f1886]) ).
fof(f98532,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98218]) ).
fof(f98218,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18239]) ).
fof(f98531,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98219]) ).
fof(f98219,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23106]) ).
fof(f23106,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(not(not(X0)),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f19252,f1066]) ).
fof(f98530,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98220]) ).
fof(f98220,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f32576]) ).
fof(f32576,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(necessarily(not(not(X0))),X1),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23214,f1066]) ).
fof(f98529,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98221]) ).
fof(f98221,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23595]) ).
fof(f23595,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(necessarily(not(not(X0)))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f20185,f1066]) ).
fof(f98528,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98222]) ).
fof(f98222,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f38267]) ).
fof(f38267,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(necessarily(necessarily(not(not(X0))))),X0))
| ~ spl1_3 ),
inference(resolution,[],[f23699,f1066]) ).
fof(f98527,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98223]) ).
fof(f98223,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f31720]) ).
fof(f31720,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(and(not(not(X0)),X1)),X0))
| ~ spl1_3 ),
inference(resolution,[],[f22659,f1066]) ).
fof(f98526,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98233]) ).
fof(f98233,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11711]) ).
fof(f11711,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(equiv(X0,X0)),X1)),
inference(forward_demodulation,[],[f11685,f289]) ).
fof(f11685,plain,
! [X0,X1] : is_a_theorem(necessarily(or(equiv(X0,X0),X1))),
inference(resolution,[],[f10234,f230]) ).
fof(f98525,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98234]) ).
fof(f98234,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12093]) ).
fof(f12093,plain,
! [X0,X1] : is_a_theorem(strict_implies(not(strict_equiv(X0,X0)),X1)),
inference(forward_demodulation,[],[f12070,f289]) ).
fof(f12070,plain,
! [X0,X1] : is_a_theorem(necessarily(or(strict_equiv(X0,X0),X1))),
inference(resolution,[],[f10257,f230]) ).
fof(f98524,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98235]) ).
fof(f98235,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2883]) ).
fof(f2883,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(not(X0),or(X1,X0)),X1)),
inference(resolution,[],[f2769,f1840]) ).
fof(f98523,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98236]) ).
fof(f98236,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f31856]) ).
fof(f31856,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,necessarily(not(not(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f23031,f1066]) ).
fof(f98522,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98246]) ).
fof(f98246,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,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,[],[f20952,f10244]) ).
fof(f98521,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98247]) ).
fof(f98247,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,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,[],[f20952,f10267]) ).
fof(f98520,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98249]) ).
fof(f98249,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f42077]) ).
fof(f42077,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(possibly(equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f24799,f1826]) ).
fof(f98519,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98250]) ).
fof(f98250,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f42102]) ).
fof(f42102,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(possibly(strict_equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f24800,f1826]) ).
fof(f98518,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98251]) ).
fof(f98251,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f31541]) ).
fof(f31541,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(and(X0,not(not(X1)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f22640,f1066]) ).
fof(f98517,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98253]) ).
fof(f98253,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f36024]) ).
fof(f36024,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(necessarily(not(equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f23592,f1843]) ).
fof(f98516,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98254]) ).
fof(f98254,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f36045]) ).
fof(f36045,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(necessarily(not(strict_equiv(X0,X0)))),X1))
| ~ spl1_3 ),
inference(resolution,[],[f23600,f1843]) ).
fof(f98515,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98259]) ).
fof(f98259,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f32251]) ).
fof(f32251,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f23103,f1843]) ).
fof(f98514,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98260]) ).
fof(f98260,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f32356]) ).
fof(f32356,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(not(strict_equiv(X0,X0)),X1),X2))
| ~ spl1_3 ),
inference(resolution,[],[f23111,f1843]) ).
fof(f98513,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98264]) ).
fof(f98264,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f35079]) ).
fof(f35079,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X0,not(equiv(X1,X1))),X2))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f35045,f218]) ).
fof(f35045,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(implies(and(X0,not(equiv(X1,X1))),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f23539,f10244]) ).
fof(f23539,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,implies(and(X1,not(X0)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f19282,f1840]) ).
fof(f98512,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98265]) ).
fof(f98265,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f35080]) ).
fof(f35080,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(and(X0,not(strict_equiv(X1,X1))),X2))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f35051,f218]) ).
fof(f35051,plain,
( ! [X2,X0,X1] : is_a_theorem(necessarily(implies(and(X0,not(strict_equiv(X1,X1))),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f23539,f10267]) ).
fof(f98511,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98266]) ).
fof(f98266,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2127]) ).
fof(f2127,plain,
! [X0,X1] : is_a_theorem(strict_implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(resolution,[],[f1826,f244]) ).
fof(f98510,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98267]) ).
fof(f98267,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19180]) ).
fof(f19180,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X0)))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f19157,f219]) ).
fof(f19157,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(and(X1,not(X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18289,f1840]) ).
fof(f98509,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98268]) ).
fof(f98268,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92729]) ).
fof(f92729,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,implies(X1,X1))),
inference(resolution,[],[f92645,f1840]) ).
fof(f98508,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98274]) ).
fof(f98274,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20952]) ).
fof(f98507,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98275]) ).
fof(f98275,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24905]) ).
fof(f24905,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(necessarily(necessarily(not(X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20957,f1840]) ).
fof(f98506,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98276]) ).
fof(f98276,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23539]) ).
fof(f98505,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98277]) ).
fof(f98277,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23559]) ).
fof(f23559,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,implies(and(not(X0),X1),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f19283,f1840]) ).
fof(f98504,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98278]) ).
fof(f98278,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19316]) ).
fof(f19316,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(necessarily(not(X0)),implies(possibly(X0),X1)))
| ~ spl1_3 ),
inference(superposition,[],[f19292,f282]) ).
fof(f19292,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,or(X0,X1)))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f19279,f278]) ).
fof(f19279,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,implies(not(X0),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f19267,f1840]) ).
fof(f98503,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98279]) ).
fof(f98279,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2125]) ).
fof(f98502,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98280]) ).
fof(f98280,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10651]) ).
fof(f10651,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,equiv(X1,X1))),
inference(resolution,[],[f10401,f1840]) ).
fof(f98501,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98282]) ).
fof(f98282,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18286]) ).
fof(f98500,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98284]) ).
fof(f98284,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28081]) ).
fof(f28081,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(not(equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f28011,f1879]) ).
fof(f1879,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f1859,f1066]) ).
fof(f98499,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98285]) ).
fof(f98285,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f28327]) ).
fof(f28327,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X0,not(not(strict_equiv(X1,X1)))))
| ~ spl1_3 ),
inference(resolution,[],[f28256,f1879]) ).
fof(f98498,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98286]) ).
fof(f98286,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19252]) ).
fof(f98497,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98287]) ).
fof(f98287,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23031]) ).
fof(f98496,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98288]) ).
fof(f98288,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23214]) ).
fof(f98495,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98289]) ).
fof(f98289,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f20185]) ).
fof(f98494,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98290]) ).
fof(f98290,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23699]) ).
fof(f98493,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98291]) ).
fof(f98291,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f22640]) ).
fof(f98492,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98292]) ).
fof(f98292,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f22659]) ).
fof(f98491,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98293]) ).
fof(f98293,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18371]) ).
fof(f18371,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(not(X0)),not(possibly(X0))))
| ~ spl1_3 ),
inference(superposition,[],[f18286,f221]) ).
fof(f98490,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98294]) ).
fof(f98294,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18433]) ).
fof(f18433,plain,
( ! [X0] : is_a_theorem(strict_implies(necessarily(not(X0)),not(necessarily(possibly(X0)))))
| ~ spl1_3 ),
inference(superposition,[],[f18407,f245]) ).
fof(f18407,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ spl1_3 ),
inference(forward_demodulation,[],[f18392,f221]) ).
fof(f18392,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,not(necessarily(not(X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18291,f1840]) ).
fof(f98489,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98295]) ).
fof(f98295,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2121]) ).
fof(f98488,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98298]) ).
fof(f98298,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11702]) ).
fof(f11702,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,and(equiv(X1,X1),X0))),
inference(forward_demodulation,[],[f11665,f218]) ).
fof(f11665,plain,
! [X0,X1] : is_a_theorem(necessarily(implies(X0,and(equiv(X1,X1),X0)))),
inference(resolution,[],[f10234,f234]) ).
fof(f98487,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98299]) ).
fof(f98299,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12084]) ).
fof(f12084,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,and(strict_equiv(X1,X1),X0))),
inference(forward_demodulation,[],[f12050,f218]) ).
fof(f12050,plain,
! [X0,X1] : is_a_theorem(necessarily(implies(X0,and(strict_equiv(X1,X1),X0)))),
inference(resolution,[],[f10257,f234]) ).
fof(f98486,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98306]) ).
fof(f98306,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19207]) ).
fof(f19207,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(X1,or(X0,X1)))
| ~ spl1_3 ),
inference(superposition,[],[f19180,f278]) ).
fof(f98485,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98307]) ).
fof(f98307,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f95562]) ).
fof(f95562,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,or(X1,not(X1)))),
inference(resolution,[],[f93869,f1840]) ).
fof(f98484,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98308]) ).
fof(f98308,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f19292]) ).
fof(f98483,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98313]) ).
fof(f98313,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18321]) ).
fof(f98482,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98316]) ).
fof(f98316,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45614]) ).
fof(f45614,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,strict_implies(not(equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41533,f1879]) ).
fof(f98481,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98317]) ).
fof(f98317,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45644]) ).
fof(f45644,plain,
( ! [X2,X0,X1] : is_a_theorem(strict_implies(X0,strict_implies(not(strict_equiv(X1,X1)),X2)))
| ~ spl1_3 ),
inference(resolution,[],[f41561,f1879]) ).
fof(f98480,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98320]) ).
fof(f98320,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2130]) ).
fof(f98479,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98321]) ).
fof(f98321,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f10729]) ).
fof(f10729,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,strict_equiv(X1,X1))),
inference(resolution,[],[f10705,f1840]) ).
fof(f98478,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98322]) ).
fof(f98322,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18407]) ).
fof(f98477,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98325]) ).
fof(f98325,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f14481]) ).
fof(f14481,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,possibly(equiv(X1,X1)))),
inference(resolution,[],[f14451,f1840]) ).
fof(f98476,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98326]) ).
fof(f98326,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f14934]) ).
fof(f14934,plain,
! [X0,X1] : is_a_theorem(strict_implies(X0,possibly(strict_equiv(X1,X1)))),
inference(resolution,[],[f14904,f1840]) ).
fof(f98475,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98327]) ).
fof(f98327,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f2660]) ).
fof(f2660,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,f248,f271,f222,f277,f279,f280,f281,f253,f254,f255,f278,f286,f287,f288,f296,f304,f305,f306,f300,f308,f309,f301,f311,f312,f302,f314,f315,f261,f285,f317,f323,f245,f332,f327,f246,f320,f336,f337,f338,f335,f340,f339,f238,f362,f341,f366,f367,f368,f289,f375,f291,f377,f378,f379,f292,f381,f382,f383,f293,f294,f390,f391,f392,f393,f297,f395,f396,f397,f298,f400,f401,f402,f299,f404,f405,f406,f407,f220,f411,f414,f408,f415,f409,f416,f412,f413,f303,f425,f426,f422,f307,f435,f436,f310,f445,f446,f313,f455,f456,f328,f223,f463,f464,f467,f468,f471,f372,f483,f484,f485,f374,f489,f490,f491,f376,f493,f494,f495,f380,f496,f497,f498,f528,f555,f557,f240,f574,f575,f266,f578,f579,f580,f581,f582,f282,f635,f636,f623,f662,f625,f681,f691,f243,f697,f695,f698,f358,f704,f711,f699,f714,f719,f700,f726,f724,f737,f703,f755,f244,f758,f759,f760,f761,f725,f763,f727,f766,f767,f734,f718,f784,f785,f786,f787,f553,f791,f792,f793,f794,f263,f799,f841,f801,f802,f842,f804,f805,f843,f807,f808,f809,f810,f811,f812,f813,f814,f815,f816,f844,f845,f846,f847,f821,f822,f823,f827,f828,f829,f830,f850,f834,f835,f836,f324,f855,f856,f857,f858,f329,f330,f890,f361,f897,f709,f756,f915,f916,f790,f918,f398,f922,f923,f924,f926,f927,f928,f321,f936,f939,f952,f583,f853,f993,f994,f995,f996,f914,f1000,f1001,f917,f1046,f1047,f1052,f1054,f1056,f1062,f1063,f1064,f1068,f1070,f1072,f1032,f1034,f1075,f1043,f275,f1137,f1138,f1080,f1139,f1087,f1145,f1089,f1146,f1147,f1092,f1093,f1148,f1095,f1096,f1097,f1098,f1099,f1100,f1101,f1102,f1103,f1104,f1149,f1150,f1151,f1152,f1109,f1110,f1153,f1112,f1154,f1114,f1118,f1119,f1120,f1121,f1122,f1123,f1157,f1127,f1128,f1129,f1131,f1044,f1164,f1167,f1177,f1168,f1008,f1186,f1188,f1185,f1012,f1202,f1203,f1201,f1208,f1209,f1205,f1207,f1214,f1215,f1023,f1232,f1234,f1231,f1024,f1243,f1245,f1242,f1048,f1262,f1257,f1258,f1259,f1260,f1261,f1252,f1180,f1269,f1271,f1276,f1277,f1278,f1279,f283,f1280,f1281,f1282,f1283,f1284,f1286,f1287,f1290,f1291,f1293,f1305,f1308,f1309,f1312,f1313,f1324,f1240,f1366,f1365,f1251,f1372,f1371,f1045,f1412,f1416,f1418,f1059,f410,f1425,f1424,f1060,f1061,f1414,f1430,f1433,f1436,f1435,f1181,f1441,f1442,f1197,f1238,f1249,f1432,f1464,f1466,f573,f1588,f1586,f1587,f999,f1593,f1596,f1597,f1592,f1604,f1608,f1644,f1645,f1646,f1647,f1648,f1649,f1620,f1621,f1650,f1651,f1652,f1653,f1654,f1631,f1632,f1633,f1635,f1636,f1638,f1643,f1629,f1657,f1658,f1622,f1661,f1662,f1623,f1665,f1666,f1605,f1678,f1680,f1618,f1619,f693,f1685,f1692,f1694,f1689,f1690,f1695,f1634,f1696,f1697,f1640,f1641,f1007,f1709,f1711,f264,f1712,f1713,f1717,f1784,f1719,f1720,f1785,f1722,f1723,f1724,f1786,f1726,f1727,f1728,f1729,f1730,f1731,f1732,f1733,f1734,f1735,f1736,f1787,f1788,f1789,f1790,f1741,f1742,f1791,f1744,f1792,f1746,f1752,f1753,f1754,f1755,f1756,f1757,f1795,f1761,f1762,f1763,f1765,f1770,f1799,f1772,f1039,f1040,f1041,f1050,f1823,f1824,f1831,f1829,f1058,f1838,f1835,f1836,f1837,f1066,f1841,f1842,f1857,f1845,f1846,f1847,f1848,f1849,f1850,f1851,f1852,f1853,f1854,f1855,f1856,f1843,f1866,f1867,f1868,f1869,f1870,f1859,f1879,f1880,f1881,f1882,f1883,f1884,f1885,f1840,f1891,f1892,f1893,f1894,f1895,f1896,f1897,f1898,f1886,f284,f1907,f1966,f1909,f1910,f1911,f1912,f1913,f1914,f1915,f1919,f1920,f1921,f1922,f1925,f1926,f1928,f1940,f1943,f1944,f1945,f1948,f1949,f1960,f1889,f1073,f2037,f2038,f2039,f2025,f2047,f2049,f322,f2067,f2069,f2056,f2057,f2058,f2059,f2060,f2061,f2062,f2063,f2064,f2065,f2066,f1415,f2074,f2075,f2076,f1826,f2128,f2129,f2135,f2136,f2121,f2141,f2142,f2125,f2146,f2130,f1834,f2160,f2161,f2155,f2156,f2157,f2158,f2159,f554,f2186,f2193,f2189,f2190,f2191,f2192,f556,f2268,f2275,f2271,f2272,f2273,f2274,f1268,f2366,f2367,f2368,f1858,f2379,f2383,f2385,f1860,f2388,f2401,f2402,f2403,f276,f2407,f2504,f2409,f2505,f2411,f2416,f2506,f2418,f2507,f2508,f2421,f2509,f2423,f2510,f2425,f2426,f2511,f2428,f2429,f2430,f2431,f2432,f2433,f2434,f2435,f2436,f2437,f2512,f2513,f2514,f2515,f2442,f2443,f2516,f2445,f2446,f2517,f2448,f2454,f2455,f2456,f2457,f2458,f2459,f2520,f2466,f2467,f2468,f2471,f2476,f2477,f2478,f2528,f2529,f2481,f2539,f2491,f2494,f2548,f2549,f2497,f2127,f2635,f2636,f2637,f2638,f2154,f2641,f2644,f2645,f2648,f2649,f2650,f2651,f2659,f2653,f2654,f2656,f2657,f2658]) ).
fof(f2658,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(or(strict_implies(X0,X0),strict_implies(X0,X0))) ),
inference(resolution,[],[f2154,f2130]) ).
fof(f2656,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(or(X1,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f2154,f1045]) ).
fof(f2654,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(or(implies(X0,X1),implies(X0,X1))) ),
inference(resolution,[],[f2154,f2127]) ).
fof(f2653,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(possibly(X1),possibly(X1)))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(resolution,[],[f2154,f2025]) ).
fof(f2659,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,[],[f2652,f282]) ).
fof(f2652,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,[],[f2154,f1860]) ).
fof(f2651,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,[],[f2154,f1858]) ).
fof(f2650,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,[],[f2154,f1058]) ).
fof(f2649,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(not(X1),not(X1)))
| ~ is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f2154,f374]) ).
fof(f2648,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(not(X1),not(X1)))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f2154,f1048]) ).
fof(f2645,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(equiv(X1,X0)) ),
inference(resolution,[],[f2154,f1240]) ).
fof(f2644,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0)
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(resolution,[],[f2154,f1251]) ).
fof(f2641,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f2154,f1886]) ).
fof(f2638,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,[],[f2127,f284]) ).
fof(f2637,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,[],[f2127,f283]) ).
fof(f2636,plain,
! [X0,X1] : is_a_theorem(strict_implies(implies(necessarily(not(X0)),X1),implies(implies(possibly(X0),necessarily(not(X0))),X1))),
inference(superposition,[],[f2127,f282]) ).
fof(f2635,plain,
! [X0,X1] : is_a_theorem(strict_implies(or(X0,X1),implies(or(not(X0),not(X0)),X1))),
inference(superposition,[],[f2127,f278]) ).
fof(f2497,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,[],[f1879,f276]) ).
fof(f2549,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,[],[f2496,f289]) ).
fof(f2496,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,[],[f1860,f276]) ).
fof(f2548,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,[],[f2495,f289]) ).
fof(f2495,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,[],[f1843,f276]) ).
fof(f2494,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,[],[f1840,f276]) ).
fof(f2491,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,[],[f1415,f276]) ).
fof(f2539,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,[],[f2488,f289]) ).
fof(f2488,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,[],[f1268,f276]) ).
fof(f2481,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,[],[f1181,f276]) ).
fof(f2529,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,[],[f2480,f289]) ).
fof(f2480,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,[],[f1180,f276]) ).
fof(f2528,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,[],[f2479,f289]) ).
fof(f2479,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,[],[f1073,f276]) ).
fof(f2478,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,[],[f1066,f276]) ).
fof(f2477,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,[],[f1066,f276]) ).
fof(f2476,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,[],[f1048,f276]) ).
fof(f2471,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,[],[f853,f276]) ).
fof(f2468,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,[],[f727,f276]) ).
fof(f2467,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,[],[f718,f276]) ).
fof(f2466,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),or(X0,and(X1,not(X2))))),
inference(superposition,[],[f714,f276]) ).
fof(f2520,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,[],[f2465,f289]) ).
fof(f2465,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,[],[f623,f276]) ).
fof(f2459,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,[],[f398,f276]) ).
fof(f2458,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,[],[f398,f276]) ).
fof(f2457,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,[],[f380,f276]) ).
fof(f2456,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,[],[f376,f276]) ).
fof(f2455,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,f276]) ).
fof(f2454,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,[],[f372,f276]) ).
fof(f2448,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,[],[f341,f276]) ).
fof(f2517,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,[],[f2447,f289]) ).
fof(f2447,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,[],[f330,f276]) ).
fof(f2446,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,[],[f324,f276]) ).
fof(f2516,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,[],[f2444,f289]) ).
fof(f2444,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,[],[f321,f276]) ).
fof(f2443,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,[],[f320,f276]) ).
fof(f2515,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,[],[f2441,f289]) ).
fof(f2441,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,[],[f313,f276]) ).
fof(f2514,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,[],[f2440,f289]) ).
fof(f2440,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,[],[f310,f276]) ).
fof(f2513,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,[],[f2439,f289]) ).
fof(f2439,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,[],[f307,f276]) ).
fof(f2512,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,[],[f2438,f289]) ).
fof(f2438,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,[],[f303,f276]) ).
fof(f2437,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),implies(X1,X2)),necessarily(possibly(or(X0,and(X1,not(X2))))))),
inference(superposition,[],[f302,f276]) ).
fof(f2436,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,[],[f301,f276]) ).
fof(f2435,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,[],[f300,f276]) ).
fof(f2434,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,[],[f299,f276]) ).
fof(f2433,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,[],[f298,f276]) ).
fof(f2432,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,[],[f297,f276]) ).
fof(f2431,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,[],[f296,f276]) ).
fof(f2430,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,[],[f294,f276]) ).
fof(f2429,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,[],[f292,f276]) ).
fof(f2428,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,[],[f291,f276]) ).
fof(f2511,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,[],[f2427,f283]) ).
fof(f2427,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,[],[f284,f276]) ).
fof(f2426,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,[],[f284,f276]) ).
fof(f2425,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,[],[f283,f276]) ).
fof(f2510,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,[],[f2424,f289]) ).
fof(f2424,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,[],[f282,f276]) ).
fof(f2423,plain,
! [X2,X3,X0,X1] : implies(or(X0,and(X1,not(X2))),X3) = or(and(not(X0),implies(X1,X2)),X3),
inference(superposition,[],[f278,f276]) ).
fof(f2509,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,[],[f2422,f263]) ).
fof(f2422,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,[],[f275,f276]) ).
fof(f2421,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,f276]) ).
fof(f2508,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,[],[f2420,f289]) ).
fof(f2420,plain,
! [X2,X0,X1] : not(necessarily(possibly(and(not(X0),implies(X1,X2))))) = possibly(necessarily(or(X0,and(X1,not(X2))))),
inference(superposition,[],[f245,f276]) ).
fof(f2507,plain,
! [X2,X3,X0,X1] : implies(or(X0,and(X1,not(X2))),X3) = or(and(not(X0),implies(X1,X2)),X3),
inference(forward_demodulation,[],[f2419,f219]) ).
fof(f2419,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,f276]) ).
fof(f2418,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,f276]) ).
fof(f2506,plain,
! [X2,X0,X1] : possibly(and(not(X0),implies(X1,X2))) = not(strict_implies(not(X0),and(X1,not(X2)))),
inference(forward_demodulation,[],[f2417,f289]) ).
fof(f2417,plain,
! [X2,X0,X1] : possibly(and(not(X0),implies(X1,X2))) = not(necessarily(or(X0,and(X1,not(X2))))),
inference(superposition,[],[f221,f276]) ).
fof(f2416,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,f276]) ).
fof(f2411,plain,
! [X2,X0,X1] : or(X2,and(not(X0),not(X1))) = not(and(not(X2),or(X0,X1))),
inference(superposition,[],[f276,f278]) ).
fof(f2505,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,[],[f2410,f264]) ).
fof(f2410,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,[],[f276,f276]) ).
fof(f2409,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,[],[f276,f264]) ).
fof(f2504,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,[],[f2408,f264]) ).
fof(f2408,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,[],[f276,f275]) ).
fof(f2407,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,[],[f276,f263]) ).
fof(f2403,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,[],[f2395,f218]) ).
fof(f2395,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,[],[f1860,f264]) ).
fof(f2402,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,[],[f2394,f289]) ).
fof(f2394,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,[],[f1860,f275]) ).
fof(f2401,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,[],[f2393,f218]) ).
fof(f2393,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,[],[f1860,f263]) ).
fof(f2388,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(resolution,[],[f1860,f261]) ).
fof(f1860,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(possibly(X0))) ),
inference(superposition,[],[f1843,f221]) ).
fof(f2385,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,[],[f2384,f218]) ).
fof(f2384,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,[],[f2382,f219]) ).
fof(f2382,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,[],[f1858,f266]) ).
fof(f2383,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(necessarily(possibly(X0)))),X1)) ),
inference(forward_demodulation,[],[f2381,f221]) ).
fof(f2381,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(necessarily(possibly(X0)))),X1))
| ~ is_a_theorem(necessarily(not(necessarily(not(X0))))) ),
inference(superposition,[],[f1858,f245]) ).
fof(f2379,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(implies(necessarily(possibly(X0)),X1)) ),
inference(resolution,[],[f1858,f261]) ).
fof(f1858,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(possibly(X0)),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1843,f329]) ).
fof(f2368,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,[],[f2357,f218]) ).
fof(f2357,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,[],[f1268,f264]) ).
fof(f2367,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,[],[f2356,f289]) ).
fof(f2356,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,[],[f1268,f275]) ).
fof(f2366,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,[],[f2355,f218]) ).
fof(f2355,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,[],[f1268,f263]) ).
fof(f1268,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(implies(possibly(X0),X1)) ),
inference(superposition,[],[f1252,f282]) ).
fof(f2274,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,[],[f556,f289]) ).
fof(f2273,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,[],[f556,f218]) ).
fof(f2271,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,[],[f556,f242]) ).
fof(f2275,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,[],[f2269,f218]) ).
fof(f2269,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,[],[f556,f917]) ).
fof(f2268,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,[],[f556,f1592]) ).
fof(f2192,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,[],[f554,f289]) ).
fof(f2189,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,[],[f554,f242]) ).
fof(f2193,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,[],[f2187,f218]) ).
fof(f2187,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,[],[f554,f917]) ).
fof(f2186,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,[],[f554,f1592]) ).
fof(f2159,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,[],[f1834,f284]) ).
fof(f2158,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,[],[f1834,f283]) ).
fof(f2157,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,[],[f1834,f282]) ).
fof(f2156,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(or(X0,X0),X1)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(resolution,[],[f1834,f358]) ).
fof(f2155,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,[],[f1834,f1826]) ).
fof(f2161,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,[],[f2152,f289]) ).
fof(f2152,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(or(X0,X0)))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1834,f917]) ).
fof(f2160,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,[],[f2151,f289]) ).
fof(f2151,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(necessarily(or(X0,X0))) ),
inference(resolution,[],[f1834,f1592]) ).
fof(f2146,plain,
! [X0] : is_a_theorem(strict_implies(or(X0,not(X0)),equiv(not(X0),not(X0)))),
inference(superposition,[],[f2125,f278]) ).
fof(f2142,plain,
! [X0] : is_a_theorem(strict_implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f2121,f223]) ).
fof(f2141,plain,
! [X0] : is_a_theorem(strict_implies(strict_implies(X0,X0),strict_equiv(X0,X0))),
inference(superposition,[],[f2121,f220]) ).
fof(f2136,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f2133,f278]) ).
fof(f2133,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,implies(not(X0),X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1826,f278]) ).
fof(f2135,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f2132,f278]) ).
fof(f2132,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(not(X0),or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1826,f278]) ).
fof(f2129,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,implies(or(X0,X0),X1))) ),
inference(resolution,[],[f1826,f914]) ).
fof(f2128,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X0,X1),X1))
| ~ is_a_theorem(implies(implies(X0,X1),X0)) ),
inference(resolution,[],[f1826,f693]) ).
fof(f2076,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,[],[f1415,f264]) ).
fof(f2075,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,[],[f1415,f275]) ).
fof(f2074,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,[],[f1415,f263]) ).
fof(f1415,plain,
! [X0,X1] :
( is_a_theorem(or(X1,and(X0,not(X1))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1045,f372]) ).
fof(f2063,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,[],[f322,f222]) ).
fof(f2062,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,[],[f322,f219]) ).
fof(f2061,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X1,implies(X2,necessarily(not(X0)))),implies(and(X2,possibly(X0)),X1))),
inference(superposition,[],[f322,f221]) ).
fof(f2060,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,[],[f322,f284]) ).
fof(f2057,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,X1)),implies(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f322,f278]) ).
fof(f2056,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(or(X2,implies(X0,X1))) ),
inference(resolution,[],[f322,f242]) ).
fof(f2069,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,[],[f2068,f218]) ).
fof(f2068,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,[],[f2054,f289]) ).
fof(f2054,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,[],[f322,f917]) ).
fof(f2067,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,[],[f2053,f289]) ).
fof(f2053,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(necessarily(or(X2,implies(X0,X1)))) ),
inference(resolution,[],[f322,f1592]) ).
fof(f2049,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,[],[f2048,f218]) ).
fof(f2048,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,[],[f2046,f219]) ).
fof(f2046,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,[],[f2025,f266]) ).
fof(f2047,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(possibly(X0)))
| is_a_theorem(strict_implies(not(necessarily(possibly(X0))),X1)) ),
inference(forward_demodulation,[],[f2045,f221]) ).
fof(f2045,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(necessarily(possibly(X0))),X1))
| ~ is_a_theorem(necessarily(not(necessarily(not(X0))))) ),
inference(superposition,[],[f2025,f245]) ).
fof(f2025,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1073,f228]) ).
fof(f2039,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,[],[f2031,f218]) ).
fof(f2031,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,[],[f1073,f264]) ).
fof(f2038,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,[],[f2030,f289]) ).
fof(f2030,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,[],[f1073,f275]) ).
fof(f2037,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,[],[f2029,f218]) ).
fof(f2029,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,[],[f1073,f263]) ).
fof(f1073,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(strict_implies(possibly(X0),X1)) ),
inference(forward_demodulation,[],[f1033,f218]) ).
fof(f1033,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(necessarily(implies(possibly(X0),X1))) ),
inference(resolution,[],[f917,f623]) ).
fof(f1889,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1840,f251]) ).
fof(f1960,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,[],[f321,f284]) ).
fof(f1949,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),not(not(X2))),or(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f324,f284]) ).
fof(f1948,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,[],[f853,f284]) ).
fof(f1945,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X0,X1),not(X2)),implies(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f317,f284]) ).
fof(f1944,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,[],[f320,f284]) ).
fof(f1943,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,[],[f1840,f284]) ).
fof(f1940,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(not(X0),not(X1)))) ),
inference(superposition,[],[f1252,f284]) ).
fof(f1928,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(and(not(X0),not(X1)))
| is_a_theorem(implies(or(X0,X1),X2)) ),
inference(superposition,[],[f251,f284]) ).
fof(f1922,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,[],[f756,f284]) ).
fof(f1921,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,[],[f914,f284]) ).
fof(f1920,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,[],[f999,f284]) ).
fof(f1919,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,[],[f1058,f284]) ).
fof(f1915,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,[],[f284,f264]) ).
fof(f1914,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,[],[f284,f275]) ).
fof(f1913,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,[],[f284,f263]) ).
fof(f1912,plain,
! [X2,X3,X0,X1] : implies(or(X2,and(not(X0),not(X1))),X3) = or(and(not(X2),or(X0,X1)),X3),
inference(superposition,[],[f284,f222]) ).
fof(f1911,plain,
! [X2,X3,X0,X1] : implies(or(X2,and(X0,not(X1))),X3) = or(and(not(X2),implies(X0,X1)),X3),
inference(superposition,[],[f284,f219]) ).
fof(f1910,plain,
! [X2,X0,X1] : implies(or(X1,necessarily(not(X0))),X2) = or(and(not(X1),possibly(X0)),X2),
inference(superposition,[],[f284,f221]) ).
fof(f1909,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,[],[f284,f264]) ).
fof(f1966,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,[],[f1908,f283]) ).
fof(f1908,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,[],[f284,f275]) ).
fof(f1907,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,[],[f284,f263]) ).
fof(f1898,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,[],[f1840,f283]) ).
fof(f1897,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(X1)))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f1840,f282]) ).
fof(f1896,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,[],[f1840,f264]) ).
fof(f1895,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,[],[f1840,f275]) ).
fof(f1894,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,[],[f1840,f263]) ).
fof(f1893,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,[],[f1840,f222]) ).
fof(f1892,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,implies(X0,X1)))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1840,f219]) ).
fof(f1891,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1840,f221]) ).
fof(f1885,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,[],[f1879,f264]) ).
fof(f1884,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,[],[f1879,f275]) ).
fof(f1883,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,[],[f1879,f263]) ).
fof(f1882,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(or(X0,X1)))
| is_a_theorem(strict_implies(X2,and(not(X0),not(X1)))) ),
inference(superposition,[],[f1879,f222]) ).
fof(f1881,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,X1)))
| is_a_theorem(strict_implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f1879,f219]) ).
fof(f1880,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,necessarily(not(X0))))
| ~ is_a_theorem(not(possibly(X0))) ),
inference(superposition,[],[f1879,f221]) ).
fof(f1870,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,[],[f1865,f218]) ).
fof(f1865,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,[],[f1843,f264]) ).
fof(f1869,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,[],[f1864,f289]) ).
fof(f1864,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,[],[f1843,f275]) ).
fof(f1868,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,[],[f1863,f218]) ).
fof(f1863,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,[],[f1843,f263]) ).
fof(f1867,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,[],[f1862,f289]) ).
fof(f1862,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| is_a_theorem(strict_implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1843,f222]) ).
fof(f1866,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(forward_demodulation,[],[f1861,f218]) ).
fof(f1861,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(strict_implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1843,f219]) ).
fof(f1856,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,[],[f1066,f264]) ).
fof(f1855,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,[],[f1066,f275]) ).
fof(f1854,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,[],[f1066,f263]) ).
fof(f1853,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,[],[f1066,f222]) ).
fof(f1852,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,[],[f1066,f219]) ).
fof(f1851,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),possibly(X0)))
| is_a_theorem(strict_implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f1066,f221]) ).
fof(f1850,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,[],[f1066,f264]) ).
fof(f1849,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,[],[f1066,f275]) ).
fof(f1848,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,[],[f1066,f263]) ).
fof(f1847,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,[],[f1066,f222]) ).
fof(f1846,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,[],[f1066,f219]) ).
fof(f1845,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(X0),not(X1)))
| is_a_theorem(strict_implies(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f1066,f221]) ).
fof(f1857,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1844,f278]) ).
fof(f1844,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(not(X1),not(X0))) ),
inference(resolution,[],[f1066,f247]) ).
fof(f1842,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X1),not(X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1066,f1240]) ).
fof(f1841,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),not(X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1066,f1251]) ).
fof(f1837,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,[],[f1058,f283]) ).
fof(f1836,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,[],[f1058,f282]) ).
fof(f1835,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,[],[f1058,f1050]) ).
fof(f1838,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,[],[f1832,f289]) ).
fof(f1832,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(or(X0,X0))) ),
inference(resolution,[],[f1058,f790]) ).
fof(f1829,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(superposition,[],[f1050,f278]) ).
fof(f1831,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(strict_implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f1828,f278]) ).
fof(f1828,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(or(X0,implies(not(X0),X1))) ),
inference(resolution,[],[f1050,f374]) ).
fof(f1824,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,implies(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1050,f1240]) ).
fof(f1823,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(implies(X0,X1),X0))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1050,f1251]) ).
fof(f1040,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(resolution,[],[f917,f408]) ).
fof(f1039,plain,
! [X0] :
( is_a_theorem(necessarily(strict_equiv(X0,X0)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X0))) ),
inference(resolution,[],[f917,f725]) ).
fof(f1772,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,[],[f1181,f264]) ).
fof(f1799,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,[],[f1771,f218]) ).
fof(f1771,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,[],[f1180,f264]) ).
fof(f1770,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,[],[f1048,f264]) ).
fof(f1765,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,[],[f853,f264]) ).
fof(f1763,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,[],[f727,f264]) ).
fof(f1762,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,[],[f718,f264]) ).
fof(f1761,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f714,f264]) ).
fof(f1795,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,[],[f1760,f218]) ).
fof(f1760,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,[],[f623,f264]) ).
fof(f1757,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,[],[f398,f264]) ).
fof(f1756,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,[],[f398,f264]) ).
fof(f1755,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,[],[f380,f264]) ).
fof(f1754,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,[],[f376,f264]) ).
fof(f1753,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(f1752,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,[],[f372,f264]) ).
fof(f1746,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,[],[f341,f264]) ).
fof(f1792,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,[],[f1745,f218]) ).
fof(f1745,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,[],[f330,f264]) ).
fof(f1744,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,[],[f324,f264]) ).
fof(f1742,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,[],[f320,f264]) ).
fof(f1790,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,[],[f1740,f218]) ).
fof(f1740,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,[],[f313,f264]) ).
fof(f1789,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,[],[f1739,f218]) ).
fof(f1739,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,[],[f310,f264]) ).
fof(f1788,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,[],[f1738,f218]) ).
fof(f1738,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,[],[f307,f264]) ).
fof(f1787,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,[],[f1737,f218]) ).
fof(f1737,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,[],[f303,f264]) ).
fof(f1736,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),necessarily(possibly(implies(X0,and(X1,not(X2))))))),
inference(superposition,[],[f302,f264]) ).
fof(f1735,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),or(implies(X0,and(X1,not(X2))),X3))),
inference(superposition,[],[f301,f264]) ).
fof(f1734,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),or(X3,implies(X0,and(X1,not(X2)))))),
inference(superposition,[],[f300,f264]) ).
fof(f1733,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,[],[f299,f264]) ).
fof(f1732,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,[],[f298,f264]) ).
fof(f1731,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,[],[f297,f264]) ).
fof(f1730,plain,
! [X2,X3,X0,X1] : is_a_theorem(or(and(X0,implies(X1,X2)),implies(X3,implies(X0,and(X1,not(X2)))))),
inference(superposition,[],[f296,f264]) ).
fof(f1729,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,[],[f294,f264]) ).
fof(f1728,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,[],[f292,f264]) ).
fof(f1727,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,[],[f291,f264]) ).
fof(f1726,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,[],[f283,f264]) ).
fof(f1786,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,[],[f1725,f218]) ).
fof(f1725,plain,
! [X2,X3,X0,X1] : implies(possibly(and(X0,implies(X1,X2))),X3) = or(necessarily(implies(X0,and(X1,not(X2)))),X3),
inference(superposition,[],[f282,f264]) ).
fof(f1724,plain,
! [X2,X3,X0,X1] : implies(implies(X0,and(X1,not(X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(superposition,[],[f278,f264]) ).
fof(f1723,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,[],[f275,f264]) ).
fof(f1722,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(f1785,plain,
! [X2,X0,X1] : not(necessarily(possibly(and(X0,implies(X1,X2))))) = possibly(strict_implies(X0,and(X1,not(X2)))),
inference(forward_demodulation,[],[f1721,f218]) ).
fof(f1721,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(f1720,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(f1719,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(f1784,plain,
! [X2,X0,X1] : not(strict_implies(X0,and(X1,not(X2)))) = possibly(and(X0,implies(X1,X2))),
inference(forward_demodulation,[],[f1718,f218]) ).
fof(f1718,plain,
! [X2,X0,X1] : possibly(and(X0,implies(X1,X2))) = not(necessarily(implies(X0,and(X1,not(X2))))),
inference(superposition,[],[f221,f264]) ).
fof(f1717,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(f1712,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
inference(superposition,[],[f264,f278]) ).
fof(f1711,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,[],[f1710,f218]) ).
fof(f1710,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,[],[f1007,f223]) ).
fof(f1709,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,[],[f1007,f220]) ).
fof(f1007,plain,
! [X0,X1] :
( is_a_theorem(necessarily(and(X1,X0)))
| ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f917,f253]) ).
fof(f1641,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X1,X0)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1592,f409]) ).
fof(f1640,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f1592,f408]) ).
fof(f1697,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1634,f1238]) ).
fof(f1696,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X1,X0))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1634,f1249]) ).
fof(f1634,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1592,f248]) ).
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,f278]) ).
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,[],[f693,f278]) ).
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,[],[f693,f278]) ).
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,[],[f693,f917]) ).
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,[],[f693,f1592]) ).
fof(f1619,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1592,f236]) ).
fof(f1618,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X1,X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1592,f235]) ).
fof(f1680,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,[],[f1679,f218]) ).
fof(f1679,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1605,f223]) ).
fof(f1678,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,[],[f1605,f220]) ).
fof(f1605,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1592,f253]) ).
fof(f1666,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f1623,f223]) ).
fof(f1665,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f1623,f220]) ).
fof(f1623,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X1,X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1592,f233]) ).
fof(f1662,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1622,f223]) ).
fof(f1661,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f1622,f220]) ).
fof(f1622,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(X0,X1)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1592,f232]) ).
fof(f1658,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[],[f1629,f289]) ).
fof(f1657,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f1629,f218]) ).
fof(f1629,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f1592,f225]) ).
fof(f1638,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1592,f294]) ).
fof(f1636,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,[],[f1592,f410]) ).
fof(f1635,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(resolution,[],[f1592,f528]) ).
fof(f1633,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(resolution,[],[f1592,f330]) ).
fof(f1632,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(resolution,[],[f1592,f623]) ).
fof(f1631,plain,
! [X0,X1] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(necessarily(X1)))
| ~ is_a_theorem(strict_implies(X1,X0)) ),
inference(resolution,[],[f1592,f553]) ).
fof(f1654,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),possibly(X0)))
| is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(forward_demodulation,[],[f1628,f289]) ).
fof(f1628,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(or(X1,possibly(X0)))) ),
inference(resolution,[],[f1592,f321]) ).
fof(f1653,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f1627,f289]) ).
fof(f1627,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(or(X0,or(X0,X1)))) ),
inference(resolution,[],[f1592,f361]) ).
fof(f1652,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f1626,f289]) ).
fof(f1626,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(or(X1,not(not(X0))))) ),
inference(resolution,[],[f1592,f324]) ).
fof(f1650,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X1),X1))
| is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0)) ),
inference(forward_demodulation,[],[f1624,f289]) ).
fof(f1624,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(or(X1,X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(resolution,[],[f1592,f914]) ).
fof(f1621,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(not(X0),X1)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1592,f292]) ).
fof(f1620,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X1,not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1592,f291]) ).
fof(f1649,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,[],[f1617,f218]) ).
fof(f1617,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X1,X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1592,f573]) ).
fof(f1648,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(forward_demodulation,[],[f1615,f218]) ).
fof(f1615,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f1592,f756]) ).
fof(f1647,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,[],[f1614,f218]) ).
fof(f1614,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,[],[f1592,f244]) ).
fof(f1646,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X2,X0))
| is_a_theorem(implies(implies(X0,X1),implies(X2,X1))) ),
inference(forward_demodulation,[],[f1613,f218]) ).
fof(f1613,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(necessarily(implies(X2,X0))) ),
inference(resolution,[],[f1592,f243]) ).
fof(f1645,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X1,X0))
| is_a_theorem(implies(implies(X0,X1),equiv(X1,X0))) ),
inference(forward_demodulation,[],[f1612,f218]) ).
fof(f1612,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),equiv(X1,X0)))
| ~ is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f1592,f240]) ).
fof(f1644,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[],[f1611,f218]) ).
fof(f1611,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(necessarily(implies(X0,implies(X0,X1)))) ),
inference(resolution,[],[f1592,f238]) ).
fof(f1608,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1592,f299]) ).
fof(f1604,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1592,f1414]) ).
fof(f1597,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,[],[f999,f283]) ).
fof(f1596,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,[],[f999,f282]) ).
fof(f1593,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f999,f1168]) ).
fof(f1587,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),equiv(X1,not(X0))))
| ~ is_a_theorem(implies(X1,not(X0))) ),
inference(superposition,[],[f573,f278]) ).
fof(f1588,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,[],[f1584,f218]) ).
fof(f1584,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,[],[f573,f917]) ).
fof(f1466,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,[],[f1465,f218]) ).
fof(f1465,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f1432,f223]) ).
fof(f1464,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,[],[f1432,f220]) ).
fof(f1249,plain,
! [X0,X1] :
( is_a_theorem(necessarily(strict_implies(X1,X0)))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(superposition,[],[f1242,f220]) ).
fof(f1238,plain,
! [X0,X1] :
( is_a_theorem(necessarily(strict_implies(X0,X1)))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(superposition,[],[f1231,f220]) ).
fof(f1197,plain,
! [X0] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X0)))
| is_a_theorem(strict_equiv(X0,X0)) ),
inference(superposition,[],[f1185,f220]) ).
fof(f1442,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,[],[f1181,f275]) ).
fof(f1441,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,[],[f1181,f263]) ).
fof(f1181,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(not(X0))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f1168,f853]) ).
fof(f1435,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f1414,f278]) ).
fof(f1436,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1434,f218]) ).
fof(f1434,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1414,f223]) ).
fof(f1433,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,[],[f1414,f220]) ).
fof(f1430,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(necessarily(and(X0,X1))) ),
inference(resolution,[],[f1414,f917]) ).
fof(f1061,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1020,f218]) ).
fof(f1020,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f917,f236]) ).
fof(f1060,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(forward_demodulation,[],[f1019,f218]) ).
fof(f1019,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f917,f235]) ).
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,[],[f410,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,[],[f410,f917]) ).
fof(f1059,plain,
! [X0] :
( is_a_theorem(necessarily(equiv(X0,X0)))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(forward_demodulation,[],[f1018,f218]) ).
fof(f1018,plain,
! [X0] :
( ~ is_a_theorem(necessarily(implies(X0,X0)))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(resolution,[],[f917,f703]) ).
fof(f1418,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1417,f218]) ).
fof(f1417,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1045,f223]) ).
fof(f1416,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,[],[f1045,f220]) ).
fof(f1412,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(and(X0,X1)))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1045,f790]) ).
fof(f1372,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f1251,f790]) ).
fof(f1366,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1240,f790]) ).
fof(f1313,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),not(not(X2))),or(X2,and(X0,not(X1))))),
inference(superposition,[],[f324,f283]) ).
fof(f1312,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,[],[f853,f283]) ).
fof(f1305,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1252,f283]) ).
fof(f1293,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f251,f283]) ).
fof(f1287,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,[],[f756,f283]) ).
fof(f1286,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,[],[f914,f283]) ).
fof(f1284,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,[],[f283,f275]) ).
fof(f1283,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(X0,possibly(X1))),X3) = or(and(X2,implies(X0,necessarily(not(X1)))),X3),
inference(superposition,[],[f283,f263]) ).
fof(f1282,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(not(X0),not(X1))),X3) = or(and(X2,or(X0,X1)),X3),
inference(superposition,[],[f283,f222]) ).
fof(f1281,plain,
! [X2,X3,X0,X1] : implies(implies(X2,and(X0,not(X1))),X3) = or(and(X2,implies(X0,X1)),X3),
inference(superposition,[],[f283,f219]) ).
fof(f1280,plain,
! [X2,X0,X1] : implies(implies(X1,necessarily(not(X0))),X2) = or(and(X1,possibly(X0)),X2),
inference(superposition,[],[f283,f221]) ).
fof(f1279,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,[],[f1275,f289]) ).
fof(f1275,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,[],[f1180,f275]) ).
fof(f1278,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,[],[f1274,f218]) ).
fof(f1274,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,necessarily(not(X1)))))
| is_a_theorem(implies(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f1180,f263]) ).
fof(f1277,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,[],[f1273,f289]) ).
fof(f1273,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X1)))
| is_a_theorem(implies(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f1180,f222]) ).
fof(f1276,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(forward_demodulation,[],[f1272,f218]) ).
fof(f1272,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f1180,f219]) ).
fof(f1271,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(necessarily(possibly(X0))) ),
inference(superposition,[],[f1180,f221]) ).
fof(f1269,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(possibly(X0)),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f1180,f329]) ).
fof(f1180,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1168,f320]) ).
fof(f1261,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,[],[f1048,f275]) ).
fof(f1260,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,[],[f1048,f263]) ).
fof(f1259,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(or(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(not(X0),not(X1)))) ),
inference(superposition,[],[f1048,f222]) ).
fof(f1258,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(implies(X0,X1),X2))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1048,f219]) ).
fof(f1257,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1048,f221]) ).
fof(f1262,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1256,f278]) ).
fof(f1256,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[],[f1048,f261]) ).
fof(f1245,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1244,f218]) ).
fof(f1244,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(superposition,[],[f1024,f223]) ).
fof(f1243,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X1,X0))) ),
inference(superposition,[],[f1024,f220]) ).
fof(f1234,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(necessarily(equiv(X0,X1))) ),
inference(forward_demodulation,[],[f1233,f218]) ).
fof(f1233,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(superposition,[],[f1023,f223]) ).
fof(f1232,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_equiv(X0,X1)))
| is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(superposition,[],[f1023,f220]) ).
fof(f1215,plain,
! [X0,X1] :
( is_a_theorem(not(strict_implies(X0,X1)))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1207,f266]) ).
fof(f1214,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(not(necessarily(possibly(X0)))) ),
inference(superposition,[],[f1207,f245]) ).
fof(f1207,plain,
! [X0] :
( is_a_theorem(possibly(X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1201,f258]) ).
fof(f1205,plain,
~ is_a_theorem(necessarily(sK0)),
inference(resolution,[],[f1201,f1164]) ).
fof(f1209,plain,
! [X0,X1] :
( is_a_theorem(necessarily(not(strict_implies(X0,X1))))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1201,f266]) ).
fof(f1208,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1201,f245]) ).
fof(f1201,plain,
! [X0] :
( is_a_theorem(necessarily(possibly(X0)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1012,f258]) ).
fof(f1203,plain,
! [X0,X1] :
( is_a_theorem(necessarily(necessarily(not(strict_implies(X0,X1)))))
| ~ is_a_theorem(necessarily(and(X0,not(X1)))) ),
inference(superposition,[],[f1012,f266]) ).
fof(f1202,plain,
! [X0] :
( is_a_theorem(necessarily(necessarily(not(necessarily(possibly(X0))))))
| ~ is_a_theorem(necessarily(necessarily(not(X0)))) ),
inference(superposition,[],[f1012,f245]) ).
fof(f1012,plain,
! [X0] :
( is_a_theorem(necessarily(necessarily(possibly(X0))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f917,f226]) ).
fof(f1185,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f1008,f258]) ).
fof(f1188,plain,
! [X0] :
( ~ is_a_theorem(strict_implies(X0,X0))
| is_a_theorem(necessarily(equiv(X0,X0))) ),
inference(forward_demodulation,[],[f1187,f218]) ).
fof(f1187,plain,
! [X0] :
( is_a_theorem(necessarily(equiv(X0,X0)))
| ~ is_a_theorem(necessarily(implies(X0,X0))) ),
inference(superposition,[],[f1008,f223]) ).
fof(f1186,plain,
! [X0] :
( is_a_theorem(necessarily(strict_equiv(X0,X0)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X0))) ),
inference(superposition,[],[f1008,f220]) ).
fof(f1008,plain,
! [X0] :
( is_a_theorem(necessarily(and(X0,X0)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f917,f700]) ).
fof(f1177,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f1167,f278]) ).
fof(f1164,plain,
~ is_a_theorem(necessarily(possibly(sK0))),
inference(resolution,[],[f1044,f224]) ).
fof(f1131,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,[],[f853,f275]) ).
fof(f1129,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,[],[f727,f275]) ).
fof(f1128,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,or(X0,necessarily(not(X1)))),implies(X2,and(not(X0),possibly(X1))))),
inference(superposition,[],[f718,f275]) ).
fof(f1127,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(X0,necessarily(not(X1))))),
inference(superposition,[],[f714,f275]) ).
fof(f1157,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,[],[f1126,f289]) ).
fof(f1126,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(or(X0,necessarily(not(X1)))),implies(possibly(and(not(X0),possibly(X1))),X2))),
inference(superposition,[],[f623,f275]) ).
fof(f1123,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,[],[f398,f275]) ).
fof(f1122,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,[],[f398,f275]) ).
fof(f1121,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,[],[f380,f275]) ).
fof(f1120,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,[],[f376,f275]) ).
fof(f1119,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,f275]) ).
fof(f1118,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,[],[f372,f275]) ).
fof(f1114,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,[],[f341,f275]) ).
fof(f1154,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,[],[f1113,f289]) ).
fof(f1113,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(or(X0,necessarily(not(X1)))),necessarily(not(necessarily(possibly(and(not(X0),possibly(X1)))))))),
inference(superposition,[],[f330,f275]) ).
fof(f1112,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,[],[f324,f275]) ).
fof(f1153,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,[],[f1111,f289]) ).
fof(f1111,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,[],[f321,f275]) ).
fof(f1110,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,[],[f320,f275]) ).
fof(f1152,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,[],[f1108,f289]) ).
fof(f1108,plain,
! [X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),necessarily(possibly(possibly(and(not(X0),possibly(X1))))))),
inference(superposition,[],[f313,f275]) ).
fof(f1151,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,[],[f1107,f289]) ).
fof(f1107,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),or(possibly(and(not(X0),possibly(X1))),X2))),
inference(superposition,[],[f310,f275]) ).
fof(f1150,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,[],[f1106,f289]) ).
fof(f1106,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),or(X2,possibly(and(not(X0),possibly(X1)))))),
inference(superposition,[],[f307,f275]) ).
fof(f1149,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,[],[f1105,f289]) ).
fof(f1105,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,necessarily(not(X1)))),implies(X2,possibly(and(not(X0),possibly(X1)))))),
inference(superposition,[],[f303,f275]) ).
fof(f1104,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),necessarily(possibly(or(X0,necessarily(not(X1))))))),
inference(superposition,[],[f302,f275]) ).
fof(f1103,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(or(X0,necessarily(not(X1))),X2))),
inference(superposition,[],[f301,f275]) ).
fof(f1102,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),or(X2,or(X0,necessarily(not(X1)))))),
inference(superposition,[],[f300,f275]) ).
fof(f1101,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(not(X0),possibly(X1)),and(X2,or(X0,necessarily(not(X1))))))),
inference(superposition,[],[f299,f275]) ).
fof(f1100,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,[],[f298,f275]) ).
fof(f1099,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),implies(X2,and(or(X0,necessarily(not(X1))),X2)))),
inference(superposition,[],[f297,f275]) ).
fof(f1098,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),possibly(X1)),implies(X2,or(X0,necessarily(not(X1)))))),
inference(superposition,[],[f296,f275]) ).
fof(f1097,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,[],[f294,f275]) ).
fof(f1096,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(or(X0,necessarily(not(X1))),X2),or(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f292,f275]) ).
fof(f1095,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,or(X0,necessarily(not(X1)))),or(and(not(X0),possibly(X1)),X2))),
inference(superposition,[],[f291,f275]) ).
fof(f1148,plain,
! [X2,X0,X1] : implies(possibly(and(not(X0),possibly(X1))),X2) = or(strict_implies(not(X0),necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f1094,f289]) ).
fof(f1094,plain,
! [X2,X0,X1] : implies(possibly(and(not(X0),possibly(X1))),X2) = or(necessarily(or(X0,necessarily(not(X1)))),X2),
inference(superposition,[],[f282,f275]) ).
fof(f1093,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = implies(or(X0,necessarily(not(X1))),X2),
inference(superposition,[],[f278,f275]) ).
fof(f1092,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(not(X0),possibly(X1)))) = possibly(and(X2,or(X0,necessarily(not(X1))))),
inference(superposition,[],[f266,f275]) ).
fof(f1147,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),possibly(X1))))) = possibly(strict_implies(not(X0),necessarily(not(X1)))),
inference(forward_demodulation,[],[f1091,f289]) ).
fof(f1091,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),possibly(X1))))) = possibly(necessarily(or(X0,necessarily(not(X1))))),
inference(superposition,[],[f245,f275]) ).
fof(f1146,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = implies(or(X0,necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f1090,f219]) ).
fof(f1090,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),X2) = not(and(or(X0,necessarily(not(X1))),not(X2))),
inference(superposition,[],[f222,f275]) ).
fof(f1089,plain,
! [X2,X0,X1] : or(X2,and(not(X0),possibly(X1))) = not(and(not(X2),or(X0,necessarily(not(X1))))),
inference(superposition,[],[f222,f275]) ).
fof(f1145,plain,
! [X0,X1] : possibly(and(not(X0),possibly(X1))) = not(strict_implies(not(X0),necessarily(not(X1)))),
inference(forward_demodulation,[],[f1088,f289]) ).
fof(f1088,plain,
! [X0,X1] : possibly(and(not(X0),possibly(X1))) = not(necessarily(or(X0,necessarily(not(X1))))),
inference(superposition,[],[f221,f275]) ).
fof(f1087,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),possibly(X1))) = not(and(X2,or(X0,necessarily(not(X1))))),
inference(superposition,[],[f219,f275]) ).
fof(f1139,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,[],[f1081,f263]) ).
fof(f1081,plain,
! [X2,X0,X1] : or(and(not(X0),possibly(X1)),necessarily(not(X2))) = not(and(or(X0,necessarily(not(X1))),possibly(X2))),
inference(superposition,[],[f275,f275]) ).
fof(f1080,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),necessarily(not(X2))) = not(and(implies(X0,necessarily(not(X1))),possibly(X2))),
inference(superposition,[],[f275,f263]) ).
fof(f1138,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),necessarily(not(X2))) = implies(or(X0,X1),necessarily(not(X2))),
inference(forward_demodulation,[],[f1079,f263]) ).
fof(f1079,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),necessarily(not(X2))) = not(and(or(X0,X1),possibly(X2))),
inference(superposition,[],[f275,f222]) ).
fof(f1137,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),necessarily(not(X2))) = implies(implies(X0,X1),necessarily(not(X2))),
inference(forward_demodulation,[],[f1078,f263]) ).
fof(f1078,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),necessarily(not(X2))) = not(and(implies(X0,X1),possibly(X2))),
inference(superposition,[],[f275,f219]) ).
fof(f1043,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(not(X0)))
| is_a_theorem(necessarily(X1)) ),
inference(superposition,[],[f917,f278]) ).
fof(f1075,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(necessarily(strict_implies(X0,X1))) ),
inference(forward_demodulation,[],[f1036,f218]) ).
fof(f1036,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(strict_implies(X0,X1)))
| is_a_theorem(necessarily(implies(necessarily(X0),necessarily(X1)))) ),
inference(resolution,[],[f917,f528]) ).
fof(f1034,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(not(X0))))
| is_a_theorem(necessarily(necessarily(not(necessarily(possibly(X0)))))) ),
inference(resolution,[],[f917,f330]) ).
fof(f1032,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(necessarily(necessarily(X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f917,f553]) ).
fof(f1072,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(necessarily(not(X1)),X0))
| ~ is_a_theorem(strict_implies(not(X0),possibly(X1))) ),
inference(forward_demodulation,[],[f1071,f218]) ).
fof(f1071,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),possibly(X1)))
| is_a_theorem(necessarily(implies(necessarily(not(X1)),X0))) ),
inference(forward_demodulation,[],[f1029,f289]) ).
fof(f1029,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,possibly(X1))))
| is_a_theorem(necessarily(implies(necessarily(not(X1)),X0))) ),
inference(resolution,[],[f917,f321]) ).
fof(f1070,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(strict_implies(not(X0),or(X0,X1))) ),
inference(forward_demodulation,[],[f1069,f289]) ).
fof(f1069,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),or(X0,X1)))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(forward_demodulation,[],[f1028,f289]) ).
fof(f1028,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,or(X0,X1))))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f917,f361]) ).
fof(f1068,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(strict_implies(not(X0),not(not(X1)))) ),
inference(forward_demodulation,[],[f1067,f289]) ).
fof(f1067,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(not(X0),not(not(X1))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(forward_demodulation,[],[f1027,f289]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,not(not(X1)))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f917,f324]) ).
fof(f1064,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,[],[f1025,f289]) ).
fof(f1025,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,X0)))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f917,f914]) ).
fof(f1063,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X0),X1))
| ~ is_a_theorem(necessarily(equiv(not(X0),X1))) ),
inference(forward_demodulation,[],[f1022,f289]) ).
fof(f1022,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(not(X0),X1)))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f917,f292]) ).
fof(f1062,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(necessarily(equiv(X0,not(X1)))) ),
inference(forward_demodulation,[],[f1021,f289]) ).
fof(f1021,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,not(X1))))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f917,f291]) ).
fof(f1056,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,[],[f1055,f218]) ).
fof(f1055,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,[],[f1016,f218]) ).
fof(f1016,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,[],[f917,f244]) ).
fof(f1054,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,[],[f1053,f218]) ).
fof(f1053,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,[],[f1015,f218]) ).
fof(f1015,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(implies(X1,X2),implies(X0,X2)))) ),
inference(resolution,[],[f917,f243]) ).
fof(f1052,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[],[f1051,f218]) ).
fof(f1051,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(necessarily(implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(forward_demodulation,[],[f1014,f218]) ).
fof(f1014,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(resolution,[],[f917,f240]) ).
fof(f1047,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),and(X0,not(X1))))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1010,f289]) ).
fof(f1010,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X1,and(X0,not(X1))))) ),
inference(resolution,[],[f917,f299]) ).
fof(f1046,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(not(X1),X0))
| ~ is_a_theorem(necessarily(X0)) ),
inference(forward_demodulation,[],[f1009,f289]) ).
fof(f1009,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(necessarily(or(X1,X0))) ),
inference(resolution,[],[f917,f229]) ).
fof(f1001,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(possibly(X0),necessarily(not(X0))),X1))
| ~ is_a_theorem(implies(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f914,f282]) ).
fof(f1000,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(or(X0,X0),X1)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(resolution,[],[f914,f358]) ).
fof(f996,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(possibly(X0),not(not(X1))))
| is_a_theorem(or(X1,necessarily(not(X0)))) ),
inference(superposition,[],[f853,f282]) ).
fof(f995,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,[],[f853,f263]) ).
fof(f994,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,[],[f853,f222]) ).
fof(f993,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(or(X2,not(implies(X0,X1))))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f853,f219]) ).
fof(f583,plain,
! [X0,X1] :
( is_a_theorem(not(strict_implies(X0,X1)))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f262,f266]) ).
fof(f936,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(or(X1,possibly(X0))) ),
inference(resolution,[],[f321,f242]) ).
fof(f928,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(X0,possibly(X1)),and(not(X2),implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f398,f263]) ).
fof(f927,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(not(X0),not(X1)),and(not(X2),or(X0,X1))))),
inference(superposition,[],[f398,f222]) ).
fof(f926,plain,
! [X2,X0,X1] : is_a_theorem(or(X2,or(and(X0,not(X1)),and(not(X2),implies(X0,X1))))),
inference(superposition,[],[f398,f219]) ).
fof(f924,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(X2,and(implies(X0,necessarily(not(X1))),not(X2))))),
inference(superposition,[],[f398,f263]) ).
fof(f923,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X2,and(or(X0,X1),not(X2))))),
inference(superposition,[],[f398,f222]) ).
fof(f922,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(X2,and(implies(X0,X1),not(X2))))),
inference(superposition,[],[f398,f219]) ).
fof(f918,plain,
! [X0,X1] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(not(X1)))
| ~ is_a_theorem(or(X1,X0)) ),
inference(resolution,[],[f790,f374]) ).
fof(f916,plain,
! [X0,X1] : is_a_theorem(implies(implies(necessarily(not(X0)),X1),implies(implies(possibly(X0),necessarily(not(X0))),X1))),
inference(superposition,[],[f756,f282]) ).
fof(f915,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),implies(or(not(X0),not(X0)),X1))),
inference(superposition,[],[f756,f278]) ).
fof(f897,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,or(X0,X1))) ),
inference(resolution,[],[f361,f242]) ).
fof(f890,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,necessarily(not(X1))),necessarily(not(necessarily(possibly(and(X0,possibly(X1)))))))),
inference(forward_demodulation,[],[f878,f218]) ).
fof(f878,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,necessarily(not(X1)))),necessarily(not(necessarily(possibly(and(X0,possibly(X1)))))))),
inference(superposition,[],[f330,f263]) ).
fof(f329,plain,
! [X0] :
( is_a_theorem(necessarily(not(necessarily(possibly(X0)))))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f249,f245]) ).
fof(f858,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),not(not(X1))),or(X1,necessarily(not(X0))))),
inference(superposition,[],[f324,f282]) ).
fof(f857,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(implies(X0,necessarily(not(X1))))),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f324,f263]) ).
fof(f856,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(or(X0,X1))),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f324,f222]) ).
fof(f855,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,not(implies(X0,X1))),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f324,f219]) ).
fof(f836,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),and(implies(X0,necessarily(not(X1))),implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f727,f263]) ).
fof(f835,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,implies(X0,necessarily(not(X1)))),implies(X2,and(X0,possibly(X1))))),
inference(superposition,[],[f718,f263]) ).
fof(f834,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f714,f263]) ).
fof(f850,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X0,necessarily(not(X1))),implies(possibly(and(X0,possibly(X1))),X2))),
inference(forward_demodulation,[],[f833,f218]) ).
fof(f833,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(implies(X0,necessarily(not(X1)))),implies(possibly(and(X0,possibly(X1))),X2))),
inference(superposition,[],[f623,f263]) ).
fof(f830,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,[],[f380,f263]) ).
fof(f829,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,[],[f376,f263]) ).
fof(f828,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(f827,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,[],[f372,f263]) ).
fof(f823,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,necessarily(not(X1)))))
| is_a_theorem(or(and(X0,possibly(X1)),X2)) ),
inference(superposition,[],[f341,f263]) ).
fof(f822,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,[],[f320,f263]) ).
fof(f847,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),necessarily(possibly(possibly(and(X0,possibly(X1))))))),
inference(forward_demodulation,[],[f820,f218]) ).
fof(f820,plain,
! [X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),necessarily(possibly(possibly(and(X0,possibly(X1))))))),
inference(superposition,[],[f313,f263]) ).
fof(f846,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),or(possibly(and(X0,possibly(X1))),X2))),
inference(forward_demodulation,[],[f819,f218]) ).
fof(f819,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),or(possibly(and(X0,possibly(X1))),X2))),
inference(superposition,[],[f310,f263]) ).
fof(f845,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),or(X2,possibly(and(X0,possibly(X1)))))),
inference(forward_demodulation,[],[f818,f218]) ).
fof(f818,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),or(X2,possibly(and(X0,possibly(X1)))))),
inference(superposition,[],[f307,f263]) ).
fof(f844,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,necessarily(not(X1))),implies(X2,possibly(and(X0,possibly(X1)))))),
inference(forward_demodulation,[],[f817,f218]) ).
fof(f817,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,necessarily(not(X1)))),implies(X2,possibly(and(X0,possibly(X1)))))),
inference(superposition,[],[f303,f263]) ).
fof(f816,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),necessarily(possibly(implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f302,f263]) ).
fof(f815,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(implies(X0,necessarily(not(X1))),X2))),
inference(superposition,[],[f301,f263]) ).
fof(f814,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),or(X2,implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f300,f263]) ).
fof(f813,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(X0,possibly(X1)),and(X2,implies(X0,necessarily(not(X1))))))),
inference(superposition,[],[f299,f263]) ).
fof(f812,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,[],[f298,f263]) ).
fof(f811,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X2,and(implies(X0,necessarily(not(X1))),X2)))),
inference(superposition,[],[f297,f263]) ).
fof(f810,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X2,implies(X0,necessarily(not(X1)))))),
inference(superposition,[],[f296,f263]) ).
fof(f809,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,necessarily(not(X1))),X2),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f294,f263]) ).
fof(f808,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(implies(X0,necessarily(not(X1))),X2),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f292,f263]) ).
fof(f807,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,implies(X0,necessarily(not(X1)))),or(and(X0,possibly(X1)),X2))),
inference(superposition,[],[f291,f263]) ).
fof(f843,plain,
! [X2,X0,X1] : implies(possibly(and(X0,possibly(X1))),X2) = or(strict_implies(X0,necessarily(not(X1))),X2),
inference(forward_demodulation,[],[f806,f218]) ).
fof(f806,plain,
! [X2,X0,X1] : implies(possibly(and(X0,possibly(X1))),X2) = or(necessarily(implies(X0,necessarily(not(X1)))),X2),
inference(superposition,[],[f282,f263]) ).
fof(f805,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),X2) = implies(implies(X0,necessarily(not(X1))),X2),
inference(superposition,[],[f278,f263]) ).
fof(f804,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(f842,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,possibly(X1))))) = possibly(strict_implies(X0,necessarily(not(X1)))),
inference(forward_demodulation,[],[f803,f218]) ).
fof(f803,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,possibly(X1))))) = possibly(necessarily(implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f245,f263]) ).
fof(f802,plain,
! [X2,X0,X1] : or(and(X0,possibly(X1)),X2) = not(and(implies(X0,necessarily(not(X1))),not(X2))),
inference(superposition,[],[f222,f263]) ).
fof(f801,plain,
! [X2,X0,X1] : or(X2,and(X0,possibly(X1))) = not(and(not(X2),implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f222,f263]) ).
fof(f841,plain,
! [X0,X1] : not(strict_implies(X0,necessarily(not(X1)))) = possibly(and(X0,possibly(X1))),
inference(forward_demodulation,[],[f800,f218]) ).
fof(f800,plain,
! [X0,X1] : possibly(and(X0,possibly(X1))) = not(necessarily(implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f221,f263]) ).
fof(f799,plain,
! [X2,X0,X1] : implies(X2,and(X0,possibly(X1))) = not(and(X2,implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f219,f263]) ).
fof(f794,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,[],[f553,f289]) ).
fof(f793,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,[],[f553,f218]) ).
fof(f792,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,[],[f553,f289]) ).
fof(f791,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,[],[f553,f218]) ).
fof(f787,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X0,X1))),
inference(superposition,[],[f718,f278]) ).
fof(f786,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,or(X0,X1)),implies(X2,and(not(X0),not(X1))))),
inference(superposition,[],[f718,f222]) ).
fof(f785,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X2,implies(X0,X1)),implies(X2,and(X0,not(X1))))),
inference(superposition,[],[f718,f219]) ).
fof(f784,plain,
! [X0,X1] : is_a_theorem(or(and(X1,possibly(X0)),implies(X1,necessarily(not(X0))))),
inference(superposition,[],[f718,f221]) ).
fof(f734,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(superposition,[],[f724,f220]) ).
fof(f767,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),and(or(X0,X1),or(X0,X1)))),
inference(superposition,[],[f727,f222]) ).
fof(f766,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),and(implies(X0,X1),implies(X0,X1)))),
inference(superposition,[],[f727,f219]) ).
fof(f763,plain,
! [X0] :
( is_a_theorem(strict_equiv(X0,X0))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(resolution,[],[f725,f242]) ).
fof(f758,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(f726,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[],[f700,f223]) ).
fof(f719,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X0,X1))),
inference(superposition,[],[f714,f222]) ).
fof(f711,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,or(X0,X1))) ),
inference(forward_demodulation,[],[f710,f278]) ).
fof(f710,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,or(X0,X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(forward_demodulation,[],[f707,f278]) ).
fof(f707,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,implies(not(X0),X1)))
| is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f358,f278]) ).
fof(f704,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),implies(X0,X0))),
inference(resolution,[],[f358,f243]) ).
fof(f698,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X2),implies(implies(X2,X1),or(X0,X1)))),
inference(forward_demodulation,[],[f696,f278]) ).
fof(f696,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(not(X0),X2),implies(implies(X2,X1),or(X0,X1)))),
inference(superposition,[],[f243,f278]) ).
fof(f691,plain,
~ is_a_theorem(not(possibly(sK0))),
inference(resolution,[],[f681,f228]) ).
fof(f681,plain,
~ is_a_theorem(necessarily(not(possibly(sK0)))),
inference(resolution,[],[f625,f268]) ).
fof(f625,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f251,f282]) ).
fof(f662,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f623,f242]) ).
fof(f582,plain,
! [X0,X1] :
( is_a_theorem(necessarily(not(strict_implies(X0,X1))))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[],[f249,f266]) ).
fof(f580,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(not(X0),not(X1)))) = possibly(and(X2,or(X0,X1))),
inference(superposition,[],[f266,f222]) ).
fof(f579,plain,
! [X2,X0,X1] : not(strict_implies(X2,and(X0,not(X1)))) = possibly(and(X2,implies(X0,X1))),
inference(superposition,[],[f266,f219]) ).
fof(f578,plain,
! [X0,X1] : not(strict_implies(X1,necessarily(not(X0)))) = possibly(and(X1,possibly(X0))),
inference(superposition,[],[f266,f221]) ).
fof(f557,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(X2,or(X0,X1)),implies(necessarily(X2),strict_implies(not(X0),X1)))),
inference(superposition,[],[f528,f289]) ).
fof(f555,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),implies(strict_implies(not(X0),X1),necessarily(X2)))),
inference(superposition,[],[f528,f289]) ).
fof(f498,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(or(X0,X1),X2))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f380,f222]) ).
fof(f497,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(implies(X0,X1),X2))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f380,f219]) ).
fof(f496,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(possibly(X0),X1))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f380,f221]) ).
fof(f380,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f292,f242]) ).
fof(f495,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X2,or(X0,X1)))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f376,f222]) ).
fof(f494,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(equiv(X2,implies(X0,X1)))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f376,f219]) ).
fof(f493,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X1,possibly(X0)))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f376,f221]) ).
fof(f376,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X1,not(X0)))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[],[f291,f242]) ).
fof(f491,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(f490,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(f489,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(possibly(X0),X1))
| ~ is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f374,f221]) ).
fof(f485,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,[],[f372,f222]) ).
fof(f484,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(strict_implies(implies(X0,X1),X2))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f372,f219]) ).
fof(f483,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_implies(possibly(X0),X1))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f372,f221]) ).
fof(f471,plain,
! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0)) ),
inference(superposition,[],[f285,f223]) ).
fof(f468,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[],[f253,f223]) ).
fof(f467,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(superposition,[],[f234,f223]) ).
fof(f328,plain,
! [X0] :
( is_a_theorem(not(necessarily(possibly(X0))))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f262,f245]) ).
fof(f456,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),necessarily(possibly(possibly(and(not(X0),not(X1))))))),
inference(forward_demodulation,[],[f451,f289]) ).
fof(f451,plain,
! [X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),necessarily(possibly(possibly(and(not(X0),not(X1))))))),
inference(superposition,[],[f313,f222]) ).
fof(f455,plain,
! [X0,X1] : is_a_theorem(or(strict_implies(X0,X1),necessarily(possibly(possibly(and(X0,not(X1))))))),
inference(forward_demodulation,[],[f450,f218]) ).
fof(f450,plain,
! [X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),necessarily(possibly(possibly(and(X0,not(X1))))))),
inference(superposition,[],[f313,f219]) ).
fof(f446,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),or(possibly(and(not(X0),not(X1))),X2))),
inference(forward_demodulation,[],[f441,f289]) ).
fof(f441,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),or(possibly(and(not(X0),not(X1))),X2))),
inference(superposition,[],[f310,f222]) ).
fof(f445,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),or(possibly(and(X0,not(X1))),X2))),
inference(forward_demodulation,[],[f440,f218]) ).
fof(f440,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),or(possibly(and(X0,not(X1))),X2))),
inference(superposition,[],[f310,f219]) ).
fof(f436,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),or(X2,possibly(and(not(X0),not(X1)))))),
inference(forward_demodulation,[],[f431,f289]) ).
fof(f431,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),or(X2,possibly(and(not(X0),not(X1)))))),
inference(superposition,[],[f307,f222]) ).
fof(f435,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),or(X2,possibly(and(X0,not(X1)))))),
inference(forward_demodulation,[],[f430,f218]) ).
fof(f430,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),or(X2,possibly(and(X0,not(X1)))))),
inference(superposition,[],[f307,f219]) ).
fof(f422,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X1)),or(X0,possibly(X1)))),
inference(superposition,[],[f303,f278]) ).
fof(f426,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(not(X0),X1),implies(X2,possibly(and(not(X0),not(X1)))))),
inference(forward_demodulation,[],[f420,f289]) ).
fof(f420,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),implies(X2,possibly(and(not(X0),not(X1)))))),
inference(superposition,[],[f303,f222]) ).
fof(f425,plain,
! [X2,X0,X1] : is_a_theorem(or(strict_implies(X0,X1),implies(X2,possibly(and(X0,not(X1)))))),
inference(forward_demodulation,[],[f419,f218]) ).
fof(f419,plain,
! [X2,X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),implies(X2,possibly(and(X0,not(X1)))))),
inference(superposition,[],[f303,f219]) ).
fof(f413,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[],[f257,f220]) ).
fof(f412,plain,
! [X0,X1] :
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[],[f256,f220]) ).
fof(f416,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_equiv(X1,X0)) ),
inference(resolution,[],[f409,f242]) ).
fof(f415,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[],[f408,f242]) ).
fof(f414,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,[],[f285,f220]) ).
fof(f411,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(f407,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,and(not(X0),not(X1))))),
inference(superposition,[],[f299,f278]) ).
fof(f406,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(not(X0),not(X1)),and(X2,or(X0,X1))))),
inference(superposition,[],[f299,f222]) ).
fof(f405,plain,
! [X2,X0,X1] : is_a_theorem(implies(X2,or(and(X0,not(X1)),and(X2,implies(X0,X1))))),
inference(superposition,[],[f299,f219]) ).
fof(f404,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(necessarily(not(X0)),and(X1,possibly(X0))))),
inference(superposition,[],[f299,f221]) ).
fof(f402,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(not(X0),not(X1)),and(X2,or(X0,X1))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f298,f222]) ).
fof(f401,plain,
! [X2,X0,X1] :
( is_a_theorem(or(and(X0,not(X1)),and(X2,implies(X0,X1))))
| ~ is_a_theorem(X2) ),
inference(superposition,[],[f298,f219]) ).
fof(f400,plain,
! [X0,X1] :
( is_a_theorem(or(necessarily(not(X0)),and(X1,possibly(X0))))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f298,f221]) ).
fof(f298,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f253,f278]) ).
fof(f397,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),implies(X2,and(or(X0,X1),X2)))),
inference(superposition,[],[f297,f222]) ).
fof(f396,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X2,and(implies(X0,X1),X2)))),
inference(superposition,[],[f297,f219]) ).
fof(f395,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),implies(X1,and(possibly(X0),X1)))),
inference(superposition,[],[f297,f221]) ).
fof(f393,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(or(X0,X1),X2),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f294,f222]) ).
fof(f392,plain,
! [X2,X0,X1] : is_a_theorem(implies(strict_implies(implies(X0,X1),X2),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f294,f219]) ).
fof(f391,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(possibly(X0),X1),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f294,f221]) ).
fof(f390,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(strict_implies(not(X0),X1)) ),
inference(resolution,[],[f294,f242]) ).
fof(f293,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f242,f278]) ).
fof(f383,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(or(X0,X1),X2),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f292,f222]) ).
fof(f382,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(implies(X0,X1),X2),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f292,f219]) ).
fof(f381,plain,
! [X0,X1] : is_a_theorem(implies(equiv(possibly(X0),X1),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f292,f221]) ).
fof(f379,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,or(X0,X1)),or(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f291,f222]) ).
fof(f378,plain,
! [X2,X0,X1] : is_a_theorem(implies(equiv(X2,implies(X0,X1)),or(and(X0,not(X1)),X2))),
inference(superposition,[],[f291,f219]) ).
fof(f377,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X1,possibly(X0)),or(necessarily(not(X0)),X1))),
inference(superposition,[],[f291,f221]) ).
fof(f375,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f225,f289]) ).
fof(f368,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(or(X0,X1)))
| is_a_theorem(or(and(not(X0),not(X1)),X2)) ),
inference(superposition,[],[f341,f222]) ).
fof(f367,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(not(implies(X0,X1)))
| is_a_theorem(or(and(X0,not(X1)),X2)) ),
inference(superposition,[],[f341,f219]) ).
fof(f366,plain,
! [X0,X1] :
( ~ is_a_theorem(not(possibly(X0)))
| is_a_theorem(or(necessarily(not(X0)),X1)) ),
inference(superposition,[],[f341,f221]) ).
fof(f362,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[],[f360,f278]) ).
fof(f360,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),or(X0,X1)),or(X0,X1))),
inference(superposition,[],[f238,f278]) ).
fof(f339,plain,
! [X0,X1] :
( ~ is_a_theorem(not(X0))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f335,f242]) ).
fof(f340,plain,
~ is_a_theorem(not(possibly(possibly(sK0)))),
inference(resolution,[],[f335,f268]) ).
fof(f338,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(not(X0),not(X1)),X2))
| ~ is_a_theorem(or(X2,or(X0,X1))) ),
inference(superposition,[],[f320,f222]) ).
fof(f337,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(and(X0,not(X1)),X2))
| ~ is_a_theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[],[f320,f219]) ).
fof(f336,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(not(X0)),X1))
| ~ is_a_theorem(or(X1,possibly(X0))) ),
inference(superposition,[],[f320,f221]) ).
fof(f327,plain,
! [X0,X1] : not(necessarily(possibly(and(not(X0),not(X1))))) = possibly(necessarily(or(X0,X1))),
inference(superposition,[],[f245,f222]) ).
fof(f332,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,not(X1))))) = possibly(strict_implies(X0,X1)),
inference(forward_demodulation,[],[f326,f218]) ).
fof(f326,plain,
! [X0,X1] : not(necessarily(possibly(and(X0,not(X1))))) = possibly(necessarily(implies(X0,X1))),
inference(superposition,[],[f245,f219]) ).
fof(f315,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),necessarily(possibly(or(X0,X1))))),
inference(superposition,[],[f302,f222]) ).
fof(f314,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),necessarily(possibly(implies(X0,X1))))),
inference(superposition,[],[f302,f219]) ).
fof(f312,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(or(X0,X1),X2))),
inference(superposition,[],[f301,f222]) ).
fof(f311,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(implies(X0,X1),X2))),
inference(superposition,[],[f301,f219]) ).
fof(f309,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X2,or(X0,X1)))),
inference(superposition,[],[f300,f222]) ).
fof(f308,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),or(X2,implies(X0,X1)))),
inference(superposition,[],[f300,f219]) ).
fof(f306,plain,
! [X0,X1] : is_a_theorem(or(X1,or(X0,not(X1)))),
inference(superposition,[],[f296,f278]) ).
fof(f305,plain,
! [X2,X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),implies(X2,or(X0,X1)))),
inference(superposition,[],[f296,f222]) ).
fof(f304,plain,
! [X2,X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X2,implies(X0,X1)))),
inference(superposition,[],[f296,f219]) ).
fof(f288,plain,
! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(superposition,[],[f278,f222]) ).
fof(f287,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[],[f278,f219]) ).
fof(f286,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(superposition,[],[f278,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(f281,plain,
! [X0,X1] : possibly(and(not(X0),not(X1))) = not(necessarily(or(X0,X1))),
inference(superposition,[],[f221,f222]) ).
fof(f279,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f219,f222]) ).
fof(f271,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[],[f248,f242]) ).
fof(f270,plain,
~ is_a_theorem(sK0),
inference(resolution,[],[f269,f262]) ).
fof(f269,plain,
~ is_a_theorem(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(f98474,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98331]) ).
fof(f98331,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11848]) ).
fof(f11848,plain,
! [X0] : is_a_theorem(possibly(implies(X0,X0))),
inference(resolution,[],[f10235,f235]) ).
fof(f10235,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f9803,f6768]) ).
fof(f6768,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(possibly(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f6061,f242]) ).
fof(f6061,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,possibly(X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f6033,f1689]) ).
fof(f98473,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98343]) ).
fof(f98343,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11856]) ).
fof(f11856,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,equiv(X1,X1)))),
inference(resolution,[],[f10235,f231]) ).
fof(f98472,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98345]) ).
fof(f98345,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11857]) ).
fof(f11857,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,and(equiv(X1,X1),X0)))),
inference(resolution,[],[f10235,f234]) ).
fof(f98471,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98346]) ).
fof(f98346,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12190]) ).
fof(f12190,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,and(strict_equiv(X1,X1),X0)))),
inference(resolution,[],[f10258,f234]) ).
fof(f10258,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(strict_equiv(X1,X1),X0))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f9815,f6768]) ).
fof(f98470,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98347]) ).
fof(f98347,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12189]) ).
fof(f12189,plain,
! [X0,X1] : is_a_theorem(possibly(implies(X0,strict_equiv(X1,X1)))),
inference(resolution,[],[f10258,f231]) ).
fof(f98469,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98349]) ).
fof(f98349,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24849]) ).
fof(f24849,plain,
( ! [X0,X1] : is_a_theorem(possibly(implies(necessarily(not(equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20953,f10235]) ).
fof(f98468,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98350]) ).
fof(f98350,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f24853]) ).
fof(f24853,plain,
( ! [X0,X1] : is_a_theorem(possibly(implies(necessarily(not(strict_equiv(X0,X0))),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f20953,f10258]) ).
fof(f98467,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98352]) ).
fof(f98352,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f7104]) ).
fof(f7104,plain,
! [X0] : is_a_theorem(possibly(equiv(X0,X0))),
inference(subsumption_resolution,[],[f7041,f699]) ).
fof(f7041,plain,
! [X0] :
( is_a_theorem(possibly(equiv(X0,X0)))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f6768,f703]) ).
fof(f98466,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98356]) ).
fof(f98356,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18111]) ).
fof(f18111,plain,
( ! [X0] : is_a_theorem(possibly(not(not(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f10235]) ).
fof(f98465,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98357]) ).
fof(f98357,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f18115]) ).
fof(f18115,plain,
( ! [X0] : is_a_theorem(possibly(not(not(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f18092,f10258]) ).
fof(f98464,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98359]) ).
fof(f98359,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23161]) ).
fof(f23161,plain,
( ! [X0,X1] : is_a_theorem(possibly(not(and(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f10235]) ).
fof(f98463,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98360]) ).
fof(f98360,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23165]) ).
fof(f23165,plain,
( ! [X0,X1] : is_a_theorem(possibly(not(and(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f19253,f10258]) ).
fof(f98462,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98362]) ).
fof(f98362,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23648]) ).
fof(f23648,plain,
( ! [X0] : is_a_theorem(possibly(not(necessarily(necessarily(not(equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f10235]) ).
fof(f98461,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98363]) ).
fof(f98363,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f23652]) ).
fof(f23652,plain,
( ! [X0] : is_a_theorem(possibly(not(necessarily(necessarily(not(strict_equiv(X0,X0)))))))
| ~ spl1_3 ),
inference(resolution,[],[f20186,f10258]) ).
fof(f98460,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98372]) ).
fof(f98372,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11862]) ).
fof(f11862,plain,
! [X0] : is_a_theorem(possibly(and(equiv(X0,X0),equiv(X0,X0)))),
inference(resolution,[],[f10235,f700]) ).
fof(f98459,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98373]) ).
fof(f98373,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11865]) ).
fof(f11865,plain,
! [X0,X1] : is_a_theorem(possibly(and(equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10235,f10384]) ).
fof(f98458,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98375]) ).
fof(f98375,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12198]) ).
fof(f12198,plain,
! [X0,X1] : is_a_theorem(possibly(and(equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10258,f10384]) ).
fof(f98457,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98376]) ).
fof(f98376,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12195]) ).
fof(f12195,plain,
! [X0] : is_a_theorem(possibly(and(strict_equiv(X0,X0),strict_equiv(X0,X0)))),
inference(resolution,[],[f10258,f700]) ).
fof(f98456,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98377]) ).
fof(f98377,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12199]) ).
fof(f12199,plain,
! [X0,X1] : is_a_theorem(possibly(and(strict_equiv(X0,X0),strict_equiv(X1,X1)))),
inference(resolution,[],[f10258,f10688]) ).
fof(f98455,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98379]) ).
fof(f98379,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11866]) ).
fof(f11866,plain,
! [X0,X1] : is_a_theorem(possibly(and(strict_equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f10235,f10688]) ).
fof(f98454,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98387]) ).
fof(f98387,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11871]) ).
fof(f11871,plain,
! [X0,X1] : is_a_theorem(possibly(or(X0,equiv(X1,X1)))),
inference(resolution,[],[f10235,f229]) ).
fof(f98453,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98388]) ).
fof(f98388,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11850]) ).
fof(f11850,plain,
! [X0] : is_a_theorem(possibly(or(X0,not(X0)))),
inference(resolution,[],[f10235,f291]) ).
fof(f98452,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98390]) ).
fof(f98390,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12204]) ).
fof(f12204,plain,
! [X0,X1] : is_a_theorem(possibly(or(X0,strict_equiv(X1,X1)))),
inference(resolution,[],[f10258,f229]) ).
fof(f98451,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98391]) ).
fof(f98391,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11877]) ).
fof(f11877,plain,
! [X0,X1] : is_a_theorem(possibly(or(equiv(X0,X0),X1))),
inference(resolution,[],[f10235,f230]) ).
fof(f98450,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98392]) ).
fof(f98392,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12210]) ).
fof(f12210,plain,
! [X0,X1] : is_a_theorem(possibly(or(strict_equiv(X0,X0),X1))),
inference(resolution,[],[f10258,f230]) ).
fof(f98449,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98396]) ).
fof(f98396,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11878]) ).
fof(f11878,plain,
! [X0] : is_a_theorem(possibly(necessarily(possibly(equiv(X0,X0))))),
inference(resolution,[],[f10235,f226]) ).
fof(f98448,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98397]) ).
fof(f98397,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12211]) ).
fof(f12211,plain,
! [X0] : is_a_theorem(possibly(necessarily(possibly(strict_equiv(X0,X0))))),
inference(resolution,[],[f10258,f226]) ).
fof(f98447,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98404]) ).
fof(f98404,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12183]) ).
fof(f12183,plain,
! [X0] : is_a_theorem(possibly(strict_implies(X0,X0))),
inference(resolution,[],[f10258,f408]) ).
fof(f98446,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98406]) ).
fof(f98406,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45618]) ).
fof(f45618,plain,
( ! [X0,X1] : is_a_theorem(possibly(strict_implies(not(equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f41533,f18499]) ).
fof(f18499,plain,
( ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(possibly(X0)) )
| ~ spl1_3 ),
inference(resolution,[],[f18402,f2937]) ).
fof(f98445,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98407]) ).
fof(f98407,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f45648]) ).
fof(f45648,plain,
( ! [X0,X1] : is_a_theorem(possibly(strict_implies(not(strict_equiv(X0,X0)),X1)))
| ~ spl1_3 ),
inference(resolution,[],[f41561,f18499]) ).
fof(f98444,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98408]) ).
fof(f98408,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f7108]) ).
fof(f7108,plain,
! [X0] : is_a_theorem(possibly(strict_equiv(X0,X0))),
inference(subsumption_resolution,[],[f7088,f1886]) ).
fof(f7088,plain,
! [X0] :
( is_a_theorem(possibly(strict_equiv(X0,X0)))
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(resolution,[],[f6768,f725]) ).
fof(f98443,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98413]) ).
fof(f98413,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f92662]) ).
fof(f92662,plain,
( ! [X0] : is_a_theorem(possibly(possibly(implies(X0,X0))))
| ~ spl1_3 ),
inference(resolution,[],[f92628,f20774]) ).
fof(f20774,plain,
( ! [X0] :
( ~ is_a_theorem(or(possibly(X0),X0))
| is_a_theorem(possibly(possibly(X0))) )
| ~ spl1_3 ),
inference(resolution,[],[f18417,f6780]) ).
fof(f6780,plain,
! [X0,X1] :
( is_a_theorem(or(X0,possibly(X1)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[],[f6779,f278]) ).
fof(f6779,plain,
! [X0,X1] :
( is_a_theorem(or(X0,possibly(X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[],[f6061,f278]) ).
fof(f18417,plain,
( ! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(possibly(X0)) )
| ~ spl1_3 ),
inference(resolution,[],[f18407,f2154]) ).
fof(f98442,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98414]) ).
fof(f98414,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f11714]) ).
fof(f11714,plain,
! [X0] : is_a_theorem(possibly(possibly(equiv(X0,X0)))),
inference(resolution,[],[f11686,f7083]) ).
fof(f7083,plain,
! [X0] :
( ~ is_a_theorem(necessarily(necessarily(X0)))
| is_a_theorem(possibly(X0)) ),
inference(resolution,[],[f6768,f6050]) ).
fof(f98441,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98416]) ).
fof(f98416,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f33799]) ).
fof(f33799,plain,
( ! [X0] : is_a_theorem(possibly(possibly(not(not(equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f20774,f28021]) ).
fof(f98440,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98417]) ).
fof(f98417,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f33800]) ).
fof(f33800,plain,
( ! [X0] : is_a_theorem(possibly(possibly(not(not(strict_equiv(X0,X0))))))
| ~ spl1_3 ),
inference(resolution,[],[f20774,f28267]) ).
fof(f98439,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98422]) ).
fof(f98422,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f93886]) ).
fof(f93886,plain,
( ! [X0] : is_a_theorem(possibly(possibly(or(X0,not(X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f93789,f20774]) ).
fof(f98438,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98427]) ).
fof(f98427,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f47185]) ).
fof(f47185,plain,
( ! [X0,X1] : is_a_theorem(possibly(possibly(strict_implies(not(equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f45619,f20774]) ).
fof(f98437,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98428]) ).
fof(f98428,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f47829]) ).
fof(f47829,plain,
( ! [X0,X1] : is_a_theorem(possibly(possibly(strict_implies(not(strict_equiv(X0,X0)),X1))))
| ~ spl1_3 ),
inference(resolution,[],[f45649,f20774]) ).
fof(f98436,plain,
~ spl1_4,
inference(avatar_contradiction_clause,[],[f98429]) ).
fof(f98429,plain,
( $false
| ~ spl1_4 ),
inference(resolution,[],[f18095,f12096]) ).
fof(f12096,plain,
! [X0] : is_a_theorem(possibly(possibly(strict_equiv(X0,X0)))),
inference(resolution,[],[f12071,f7083]) ).
fof(f98435,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98432]) ).
fof(f98432,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f33815]) ).
fof(f33815,plain,
( ! [X0] : is_a_theorem(possibly(possibly(possibly(equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f20774,f11715]) ).
fof(f98434,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f98433]) ).
fof(f98433,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(resolution,[],[f18095,f33816]) ).
fof(f33816,plain,
( ! [X0] : is_a_theorem(possibly(possibly(possibly(strict_equiv(X0,X0)))))
| ~ spl1_3 ),
inference(resolution,[],[f20774,f12097]) ).
fof(f97476,plain,
( spl1_4
| spl1_5 ),
inference(avatar_split_clause,[],[f92598,f97474,f18094]) ).
fof(f97474,plain,
( spl1_5
<=> ! [X0] : is_a_theorem(necessarily(possibly(implies(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f92598,plain,
! [X0,X1] :
( is_a_theorem(necessarily(possibly(implies(X0,X0))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f92491,f8187]) ).
fof(f8187,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(possibly(X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f5908,f242]) ).
fof(f5908,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,necessarily(possibly(X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1689,f226]) ).
fof(f18096,plain,
( spl1_3
| spl1_4 ),
inference(avatar_split_clause,[],[f18039,f18094,f18091]) ).
fof(f18039,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,not(not(X1)))) ),
inference(resolution,[],[f11323,f5927]) ).
fof(f11323,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,and(X1,not(not(X0)))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1308,f5765]) ).
fof(f348,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f339,f346,f343]) ).
fof(f343,plain,
( spl1_1
<=> ! [X1] : is_a_theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f346,plain,
( spl1_2
<=> ! [X0] :
( ~ is_a_theorem(not(X0))
| ~ is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL548+1 : TPTP v8.2.0. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 02:47:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (3407)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (3410)WARNING: value z3 for option sas not known
% 0.15/0.38 % (3411)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (3408)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (3409)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (3413)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (3414)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 % (3412)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (3410)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [2]
% 0.21/0.41 TRYING [3]
% 0.21/0.41 TRYING [4]
% 0.21/0.47 TRYING [4]
% 0.21/0.49 TRYING [5]
% 2.00/0.68 TRYING [1]
% 2.00/0.68 TRYING [2]
% 2.00/0.69 TRYING [3]
% 2.00/0.70 TRYING [5]
% 2.00/0.71 TRYING [4]
% 2.65/0.78 TRYING [6]
% 3.14/0.80 TRYING [5]
% 6.20/1.30 TRYING [6]
% 9.44/1.72 TRYING [7]
% 17.97/2.93 TRYING [6]
% 25.43/4.08 TRYING [7]
% 51.66/7.79 TRYING [8]
% 94.70/13.96 TRYING [8]
% 133.67/19.48 % (3410)First to succeed.
% 133.67/19.52 % (3410)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3407"
% 133.67/19.52 % (3410)Refutation found. Thanks to Tanya!
% 133.67/19.52 % SZS status Theorem for theBenchmark
% 133.67/19.52 % SZS output start Proof for theBenchmark
% See solution above
% 133.67/19.54 % (3410)------------------------------
% 133.67/19.54 % (3410)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 133.67/19.54 % (3410)Termination reason: Refutation
% 133.67/19.54
% 133.67/19.54 % (3410)Memory used [KB]: 68481
% 133.67/19.54 % (3410)Time elapsed: 19.125 s
% 133.67/19.54 % (3410)Instructions burned: 49517 (million)
% 133.67/19.54 % (3407)Success in time 19.13 s
%------------------------------------------------------------------------------