TSTP Solution File: LCL524+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL524+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:46:26 EDT 2024
% Result : Theorem 221.25s 32.03s
% Output : Refutation 221.25s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f158336,plain,
$false,
inference(avatar_sat_refutation,[],[f298,f310,f311,f312,f1397,f3967,f5281,f7685,f7997,f10229,f11306,f11605,f11606,f11607,f11608,f11609,f11610,f11611,f11612,f11613,f11614,f11615,f11616,f11617,f11618,f11619,f11620,f11621,f11622,f11623,f11624,f11625,f11626,f11627,f11628,f11629,f11630,f11631,f11632,f11633,f11634,f11635,f11636,f11637,f11638,f11639,f11640,f11641,f11642,f11643,f11644,f11645,f11646,f11647,f11648,f11649,f11650,f11651,f11652,f11653,f11654,f11655,f11656,f11657,f11658,f11659,f11660,f11661,f11662,f11663,f11664,f11665,f11666,f11667,f11668,f11669,f11670,f11671,f11672,f11673,f11674,f11675,f11676,f11677,f11678,f11679,f11680,f11681,f11682,f11683,f11684,f11685,f11686,f11687,f11688,f11689,f11690,f11691,f11692,f11693,f11694,f11695,f11696,f11697,f11698,f11699,f11700,f11701,f11702,f11703,f11704,f11705,f11706,f11707,f11708,f11709,f11710,f11711,f11712,f11713,f11714,f11715,f11716,f11717,f11718,f11719,f11720,f11721,f11722,f11723,f11724,f11725,f11726,f11727,f11728,f11729,f11730,f11731,f11732,f11733,f11734,f11735,f11736,f11737,f11738,f11739,f11740,f11741,f11742,f11743,f11744,f11745,f11746,f11747,f11748,f11749,f14108,f158307]) ).
fof(f158307,plain,
~ spl1_9,
inference(avatar_contradiction_clause,[],[f158306]) ).
fof(f158306,plain,
( $false
| ~ spl1_9 ),
inference(subsumption_resolution,[],[f158260,f10225]) ).
fof(f10225,plain,
( ! [X1] : is_a_theorem(implies(X1,possibly(X1)))
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f10224]) ).
fof(f10224,plain,
( spl1_9
<=> ! [X1] : is_a_theorem(implies(X1,possibly(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f158260,plain,
~ is_a_theorem(implies(sK0,possibly(sK0))),
inference(resolution,[],[f4751,f203]) ).
fof(f203,plain,
~ is_a_theorem(implies(sK0,necessarily(possibly(sK0)))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179]) ).
fof(f179,plain,
( axiom_B
| ~ is_a_theorem(implies(sK0,necessarily(possibly(sK0)))) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( axiom_B
| ~ is_a_theorem(implies(sK0,necessarily(possibly(sK0)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f128,f149]) ).
fof(f149,plain,
( ? [X0] : ~ is_a_theorem(implies(X0,necessarily(possibly(X0))))
=> ~ is_a_theorem(implies(sK0,necessarily(possibly(sK0)))) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
( axiom_B
| ? [X0] : ~ is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,plain,
( ! [X0] : is_a_theorem(implies(X0,necessarily(possibly(X0))))
=> axiom_B ),
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(f202,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178]) ).
fof(f178,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,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(f201,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177]) ).
fof(f177,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,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(f200,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176]) ).
fof(f176,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,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(f199,plain,
! [X0] : possibly(X0) = not(necessarily(not(X0))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175]) ).
fof(f175,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,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(f174,plain,
op_possibly,
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_op_possibly) ).
fof(f173,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f172,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(f171,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f170,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f169,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f168,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f167,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f166,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f165,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f164,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f163,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f162,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f161,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f160,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f159,plain,
equivalence_1,
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
equivalence_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f158,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f157,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f156,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(f155,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_necessitation) ).
fof(f154,plain,
axiom_K,
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
axiom_K,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_K) ).
fof(f153,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f152,plain,
axiom_5,
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f151,plain,
~ axiom_B,
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
~ axiom_B,
inference(flattening,[],[f83]) ).
fof(f83,negated_conjecture,
~ axiom_B,
inference(negated_conjecture,[],[f82]) ).
fof(f82,conjecture,
axiom_B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_B) ).
fof(f4751,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,necessarily(possibly(X1))))
| ~ is_a_theorem(implies(X0,possibly(X1))) ),
inference(resolution,[],[f1390,f205]) ).
fof(f205,plain,
! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181]) ).
fof(f181,plain,
! [X0] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
( axiom_5
=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(unused_predicate_definition_removal,[],[f58]) ).
fof(f58,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f204,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180]) ).
fof(f180,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,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(f1390,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f569,f220]) ).
fof(f220,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190,f214,f191,f215,f192,f216,f193,f217,f194,f218,f195,f219,f196]) ).
fof(f196,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f145]) ).
fof(f145,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,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(f219,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190,f214,f191,f215,f192,f216,f193,f217,f194,f218,f195]) ).
fof(f195,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,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(f218,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190,f214,f191,f215,f192,f216,f193,f217,f194]) ).
fof(f194,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,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(f217,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1)))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190,f214,f191,f215,f192,f216,f193]) ).
fof(f193,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( ! [X0,X1] : is_a_theorem(implies(necessarily(implies(X0,X1)),implies(necessarily(X0),necessarily(X1))))
| ~ axiom_K ),
inference(ennf_transformation,[],[f102]) ).
fof(f102,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(f216,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190,f214,f191,f215,f192]) ).
fof(f192,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,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(f215,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190,f214,f191]) ).
fof(f191,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f116]) ).
fof(f116,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(f214,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190]) ).
fof(f190,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,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(f213,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189]) ).
fof(f189,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,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(f212,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188]) ).
fof(f188,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,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(f211,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187]) ).
fof(f187,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,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(f210,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186]) ).
fof(f186,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,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(f209,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185]) ).
fof(f185,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,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(f208,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184]) ).
fof(f184,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,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(f207,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183]) ).
fof(f183,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,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(f206,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182]) ).
fof(f182,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,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(f569,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(X2,X1)))
| ~ is_a_theorem(implies(X2,X0)) ),
inference(resolution,[],[f221,f220]) ).
fof(f221,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190,f214,f191,f215,f192,f216,f193,f217,f194,f218,f195,f219,f196,f220,f197]) ).
fof(f197,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,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(f14108,plain,
( spl1_12
| spl1_10 ),
inference(avatar_split_clause,[],[f13664,f10227,f14106]) ).
fof(f14106,plain,
( spl1_12
<=> ! [X1] : is_a_theorem(implies(X1,not(not(X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f10227,plain,
( spl1_10
<=> ! [X0] : ~ is_a_theorem(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f13664,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,not(not(X1)))) ),
inference(resolution,[],[f10161,f4731]) ).
fof(f4731,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X2,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1390,f211]) ).
fof(f10161,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,and(X1,not(not(X0)))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1159,f4601]) ).
fof(f4601,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f1386,f226]) ).
fof(f226,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f220,f209]) ).
fof(f1386,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),X0))
| is_a_theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[],[f569,f342]) ).
fof(f342,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f216,f220]) ).
fof(f1159,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(implies(X0,X1),not(X2)))
| is_a_theorem(implies(X2,and(X0,not(X1)))) ),
inference(superposition,[],[f326,f260]) ).
fof(f260,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(forward_demodulation,[],[f249,f200]) ).
fof(f249,plain,
! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2))),
inference(superposition,[],[f201,f200]) ).
fof(f326,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f291,f220]) ).
fof(f291,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(forward_demodulation,[],[f215,f254]) ).
fof(f254,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(superposition,[],[f201,f200]) ).
fof(f11749,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11307]) ).
fof(f11307,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f498]) ).
fof(f498,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[],[f342,f209]) ).
fof(f10228,plain,
( ! [X0] : ~ is_a_theorem(X0)
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f10227]) ).
fof(f11748,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11311]) ).
fof(f11311,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f209]) ).
fof(f11747,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11312]) ).
fof(f11312,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f212]) ).
fof(f11746,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11317]) ).
fof(f11317,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7083]) ).
fof(f7083,plain,
! [X0,X1] : is_a_theorem(implies(X0,equiv(X1,X1))),
inference(subsumption_resolution,[],[f6996,f498]) ).
fof(f6996,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,equiv(X1,X1)))
| ~ is_a_theorem(implies(X1,X1)) ),
inference(resolution,[],[f5298,f520]) ).
fof(f520,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f218,f342]) ).
fof(f5298,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f4704,f220]) ).
fof(f4704,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X2)))
| ~ is_a_theorem(implies(X0,X2)) ),
inference(resolution,[],[f1390,f209]) ).
fof(f11745,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11321]) ).
fof(f11321,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f499]) ).
fof(f499,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[],[f342,f212]) ).
fof(f11744,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11322]) ).
fof(f11322,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7331]) ).
fof(f7331,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),X0))),
inference(resolution,[],[f7145,f212]) ).
fof(f7145,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f7141,f644]) ).
fof(f644,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f640,f220]) ).
fof(f640,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f633,f220]) ).
fof(f633,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(resolution,[],[f222,f342]) ).
fof(f222,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))),
inference(global_subsumption,[],[f151,f152,f153,f154,f155,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f166,f167,f168,f169,f170,f171,f172,f173,f174,f175,f199,f176,f200,f177,f201,f178,f202,f179,f203,f180,f204,f181,f205,f182,f206,f183,f207,f184,f208,f185,f209,f186,f210,f187,f211,f188,f212,f189,f213,f190,f214,f191,f215,f192,f216,f193,f217,f194,f218,f195,f219,f196,f220,f197,f221,f198]) ).
fof(f198,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,[],[f148]) ).
fof(f148,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,[],[f107]) ).
fof(f107,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(f7141,plain,
! [X0,X1] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[],[f7083,f254]) ).
fof(f11743,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11326]) ).
fof(f11326,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f10190]) ).
fof(f10190,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),possibly(X0)))),
inference(forward_demodulation,[],[f10168,f199]) ).
fof(f10168,plain,
! [X0,X1] : is_a_theorem(implies(X0,and(equiv(X1,X1),not(necessarily(not(X0)))))),
inference(resolution,[],[f1159,f7225]) ).
fof(f7225,plain,
! [X0,X1] : is_a_theorem(implies(implies(equiv(X0,X0),necessarily(X1)),X1)),
inference(resolution,[],[f7140,f4744]) ).
fof(f4744,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,necessarily(X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1390,f204]) ).
fof(f7140,plain,
! [X0,X1] : is_a_theorem(implies(implies(equiv(X0,X0),X1),X1)),
inference(resolution,[],[f7083,f1386]) ).
fof(f11742,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11327]) ).
fof(f11327,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f207]) ).
fof(f11741,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11328]) ).
fof(f11328,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f208]) ).
fof(f11740,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11329]) ).
fof(f11329,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f273]) ).
fof(f273,plain,
! [X0,X1] : is_a_theorem(implies(X1,or(X0,and(X1,not(X0))))),
inference(superposition,[],[f212,f254]) ).
fof(f11739,plain,
( ~ spl1_9
| ~ spl1_10 ),
inference(avatar_contradiction_clause,[],[f11336]) ).
fof(f11336,plain,
( $false
| ~ spl1_9
| ~ spl1_10 ),
inference(resolution,[],[f10228,f10225]) ).
fof(f11738,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11346]) ).
fof(f11346,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f216]) ).
fof(f11737,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11347]) ).
fof(f11347,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f218]) ).
fof(f11736,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11348]) ).
fof(f11348,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f221]) ).
fof(f11735,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11349]) ).
fof(f11349,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f222]) ).
fof(f11734,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11350]) ).
fof(f11350,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f633]) ).
fof(f11733,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11353]) ).
fof(f11353,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f571]) ).
fof(f571,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(X2,not(X0)),implies(or(X0,X1),implies(X2,X1)))),
inference(superposition,[],[f221,f254]) ).
fof(f11732,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11354]) ).
fof(f11354,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f524]) ).
fof(f524,plain,
! [X0,X1] : is_a_theorem(implies(implies(X1,not(X0)),implies(or(X0,X1),equiv(X1,not(X0))))),
inference(superposition,[],[f218,f254]) ).
fof(f11731,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11355]) ).
fof(f11355,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f520]) ).
fof(f11730,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11358]) ).
fof(f11358,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f1160]) ).
fof(f1160,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(X0,X1),not(X2)),implies(X2,and(X0,not(X1))))),
inference(superposition,[],[f291,f260]) ).
fof(f11729,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11359]) ).
fof(f11359,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7140]) ).
fof(f11728,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11360]) ).
fof(f11360,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7225]) ).
fof(f11727,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11361]) ).
fof(f11361,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2262]) ).
fof(f2262,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(or(X1,X2),not(X0)),not(and(X0,or(X1,X2))))),
inference(forward_demodulation,[],[f2261,f254]) ).
fof(f2261,plain,
! [X2,X0,X1] : is_a_theorem(implies(implies(implies(not(X1),X2),not(X0)),not(and(X0,or(X1,X2))))),
inference(forward_demodulation,[],[f2191,f260]) ).
fof(f2191,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(and(not(X1),not(X2)),not(X0)),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f291,f257]) ).
fof(f257,plain,
! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))),
inference(superposition,[],[f200,f201]) ).
fof(f11726,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11362]) ).
fof(f11362,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f466]) ).
fof(f466,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),not(X1)),implies(X1,necessarily(not(X0))))),
inference(superposition,[],[f291,f259]) ).
fof(f259,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(forward_demodulation,[],[f248,f200]) ).
fof(f248,plain,
! [X0,X1] : or(necessarily(not(X0)),X1) = not(and(possibly(X0),not(X1))),
inference(superposition,[],[f201,f199]) ).
fof(f11725,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11363]) ).
fof(f11363,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f822]) ).
fof(f822,plain,
! [X0,X1] : is_a_theorem(implies(implies(possibly(X0),possibly(X1)),implies(necessarily(not(X1)),necessarily(not(X0))))),
inference(superposition,[],[f327,f259]) ).
fof(f327,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,possibly(X0)),implies(necessarily(not(X0)),X1))),
inference(superposition,[],[f291,f199]) ).
fof(f11724,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11365]) ).
fof(f11365,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f213]) ).
fof(f11723,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11366]) ).
fof(f11366,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f214]) ).
fof(f11722,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11367]) ).
fof(f11367,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f267]) ).
fof(f267,plain,
! [X0,X1] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[],[f214,f254]) ).
fof(f11721,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11368]) ).
fof(f11368,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f268]) ).
fof(f268,plain,
! [X0,X1] : is_a_theorem(implies(equiv(X1,not(X0)),or(X0,X1))),
inference(superposition,[],[f213,f254]) ).
fof(f11720,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11369]) ).
fof(f11369,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f210]) ).
fof(f11719,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11370]) ).
fof(f11370,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f211]) ).
fof(f11718,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11371]) ).
fof(f11371,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5431]) ).
fof(f5431,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X2,equiv(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f5363,f202]) ).
fof(f5363,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,X2)),X1)),
inference(resolution,[],[f4730,f211]) ).
fof(f4730,plain,
! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[],[f1390,f210]) ).
fof(f11717,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11372]) ).
fof(f11372,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f1132]) ).
fof(f1132,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,not(X1)),implies(implies(X0,X1),X2))),
inference(superposition,[],[f207,f260]) ).
fof(f11716,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11374]) ).
fof(f11374,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f6610]) ).
fof(f6610,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,not(X1)),not(equiv(X0,X1)))),
inference(superposition,[],[f1132,f1464]) ).
fof(f1464,plain,
! [X0,X1] : not(equiv(X0,X1)) = implies(implies(X0,X1),and(X1,not(X0))),
inference(superposition,[],[f240,f202]) ).
fof(f240,plain,
! [X2,X0,X1] : implies(X2,and(X0,not(X1))) = not(and(X2,implies(X0,X1))),
inference(superposition,[],[f200,f200]) ).
fof(f11715,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11375]) ).
fof(f11375,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f6617]) ).
fof(f6617,plain,
! [X0,X1] : is_a_theorem(implies(and(X1,not(X0)),not(equiv(X0,X1)))),
inference(superposition,[],[f209,f1464]) ).
fof(f11714,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11376]) ).
fof(f11376,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5363]) ).
fof(f11713,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11377]) ).
fof(f11377,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5430]) ).
fof(f5430,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(necessarily(X1),X2)),X1)),
inference(resolution,[],[f5363,f4744]) ).
fof(f11712,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11378]) ).
fof(f11378,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5854]) ).
fof(f5854,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,X2)),X2)),
inference(resolution,[],[f4731,f211]) ).
fof(f11711,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11379]) ).
fof(f11379,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5946]) ).
fof(f5946,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,and(X1,necessarily(X2))),X2)),
inference(resolution,[],[f5854,f4744]) ).
fof(f11710,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11380]) ).
fof(f11380,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5427]) ).
fof(f5427,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(and(X1,X2),X3)),X1)),
inference(resolution,[],[f5363,f4730]) ).
fof(f11709,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11381]) ).
fof(f11381,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5856]) ).
fof(f5856,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(X0,and(and(X1,X2),X3)),X2)),
inference(resolution,[],[f4731,f5363]) ).
fof(f11708,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11382]) ).
fof(f11382,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4764]) ).
fof(f4764,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(X1)),X1)),
inference(resolution,[],[f4744,f211]) ).
fof(f11707,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11383]) ).
fof(f11383,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4804]) ).
fof(f4804,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(X1))),X1)),
inference(resolution,[],[f4764,f4744]) ).
fof(f11706,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11384]) ).
fof(f11384,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4847]) ).
fof(f4847,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,necessarily(necessarily(necessarily(X1)))),X1)),
inference(resolution,[],[f4804,f4744]) ).
fof(f11705,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11385]) ).
fof(f11385,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5364]) ).
fof(f5364,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,X2))),X1)),
inference(resolution,[],[f4730,f4764]) ).
fof(f11704,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11386]) ).
fof(f11386,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5858]) ).
fof(f5858,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(X0,necessarily(and(X1,X2))),X2)),
inference(resolution,[],[f4731,f4764]) ).
fof(f11703,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11387]) ).
fof(f11387,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5418]) ).
fof(f5418,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(equiv(X0,X1),X2),implies(X0,X1))),
inference(superposition,[],[f5362,f202]) ).
fof(f5362,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,X1),X2),X0)),
inference(resolution,[],[f4730,f210]) ).
fof(f11702,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11388]) ).
fof(f11388,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5931]) ).
fof(f5931,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(equiv(X0,X1),X2),implies(X1,X0))),
inference(superposition,[],[f5853,f202]) ).
fof(f5853,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,X1),X2),X1)),
inference(resolution,[],[f4731,f210]) ).
fof(f11701,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11389]) ).
fof(f11389,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2515]) ).
fof(f2515,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),or(X1,X0)),X1)),
inference(resolution,[],[f2239,f326]) ).
fof(f2239,plain,
! [X0,X1] : is_a_theorem(or(X1,not(and(not(X0),or(X1,X0))))),
inference(forward_demodulation,[],[f2168,f254]) ).
fof(f2168,plain,
! [X0,X1] : is_a_theorem(implies(not(X1),not(and(not(X0),or(X1,X0))))),
inference(superposition,[],[f212,f257]) ).
fof(f11700,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11390]) ).
fof(f11390,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4765]) ).
fof(f4765,plain,
! [X0,X1] : is_a_theorem(implies(and(not(X0),or(necessarily(X1),X0)),X1)),
inference(resolution,[],[f4744,f2515]) ).
fof(f11699,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11392]) ).
fof(f11392,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f1661]) ).
fof(f1661,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2))),
inference(superposition,[],[f207,f261]) ).
fof(f261,plain,
! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(forward_demodulation,[],[f250,f200]) ).
fof(f250,plain,
! [X2,X0,X1] : or(and(not(X0),not(X1)),X2) = not(and(or(X0,X1),not(X2))),
inference(superposition,[],[f201,f201]) ).
fof(f11698,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11393]) ).
fof(f11393,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2175]) ).
fof(f2175,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(not(X1),not(X2)),not(and(X0,or(X1,X2))))),
inference(superposition,[],[f209,f257]) ).
fof(f11697,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11394]) ).
fof(f11394,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5362]) ).
fof(f11696,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11395]) ).
fof(f11395,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5417]) ).
fof(f5417,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(necessarily(X0),X1),X2),X0)),
inference(resolution,[],[f5362,f4744]) ).
fof(f11695,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11396]) ).
fof(f11396,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5853]) ).
fof(f11694,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11397]) ).
fof(f11397,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5930]) ).
fof(f5930,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(and(X0,necessarily(X1)),X2),X1)),
inference(resolution,[],[f5853,f4744]) ).
fof(f11693,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11398]) ).
fof(f11398,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5414]) ).
fof(f5414,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(and(X0,X1),X2),X3),X0)),
inference(resolution,[],[f5362,f4730]) ).
fof(f11692,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11399]) ).
fof(f11399,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5863]) ).
fof(f5863,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(and(X0,X1),X2),X3),X1)),
inference(resolution,[],[f4731,f5362]) ).
fof(f11691,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11400]) ).
fof(f11400,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5926]) ).
fof(f5926,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(X0,and(X1,X2)),X3),X2)),
inference(resolution,[],[f5853,f4731]) ).
fof(f11690,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11401]) ).
fof(f11401,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5927]) ).
fof(f5927,plain,
! [X2,X3,X0,X1] : is_a_theorem(implies(and(and(X0,and(X1,X2)),X3),X1)),
inference(resolution,[],[f5853,f4730]) ).
fof(f11689,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11402]) ).
fof(f11402,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4763]) ).
fof(f4763,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(X0),X1),X0)),
inference(resolution,[],[f4744,f210]) ).
fof(f11688,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11403]) ).
fof(f11403,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4794]) ).
fof(f4794,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(X0)),X1),X0)),
inference(resolution,[],[f4763,f4744]) ).
fof(f11687,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11404]) ).
fof(f11404,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4837]) ).
fof(f4837,plain,
! [X0,X1] : is_a_theorem(implies(and(necessarily(necessarily(necessarily(X0))),X1),X0)),
inference(resolution,[],[f4794,f4744]) ).
fof(f11686,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11405]) ).
fof(f11405,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5368]) ).
fof(f5368,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,X1)),X2),X0)),
inference(resolution,[],[f4730,f4763]) ).
fof(f11685,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11406]) ).
fof(f11406,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5865]) ).
fof(f5865,plain,
! [X2,X0,X1] : is_a_theorem(implies(and(necessarily(and(X0,X1)),X2),X1)),
inference(resolution,[],[f4731,f4763]) ).
fof(f11684,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11409]) ).
fof(f11409,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f573]) ).
fof(f573,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X0,X2)))),
inference(forward_demodulation,[],[f570,f254]) ).
fof(f570,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X0),X2)))),
inference(superposition,[],[f221,f254]) ).
fof(f11683,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11410]) ).
fof(f11410,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f523]) ).
fof(f523,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,not(X0)),equiv(not(X0),X1)))),
inference(superposition,[],[f218,f254]) ).
fof(f11682,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11414]) ).
fof(f11414,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f328]) ).
fof(f328,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,implies(X0,X1)),implies(and(X0,not(X1)),X2))),
inference(superposition,[],[f291,f200]) ).
fof(f11681,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11415]) ).
fof(f11415,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f291]) ).
fof(f11680,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11416]) ).
fof(f11416,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f330]) ).
fof(f330,plain,
! [X0,X1] : is_a_theorem(implies(or(X1,not(not(X0))),or(X0,X1))),
inference(superposition,[],[f291,f254]) ).
fof(f11679,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11417]) ).
fof(f11417,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f553]) ).
fof(f553,plain,
! [X0] : is_a_theorem(implies(or(X0,not(X0)),equiv(not(X0),not(X0)))),
inference(superposition,[],[f520,f254]) ).
fof(f11678,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11418]) ).
fof(f11418,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f345]) ).
fof(f345,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[],[f343,f254]) ).
fof(f343,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,implies(not(X0),X1)),implies(not(X0),X1))),
inference(superposition,[],[f216,f254]) ).
fof(f11677,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11419]) ).
fof(f11419,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f329]) ).
fof(f329,plain,
! [X2,X0,X1] : is_a_theorem(implies(or(X2,or(X0,X1)),implies(and(not(X0),not(X1)),X2))),
inference(superposition,[],[f291,f201]) ).
fof(f11676,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11421]) ).
fof(f11421,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f327]) ).
fof(f11675,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11422]) ).
fof(f11422,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f204]) ).
fof(f11674,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11423]) ).
fof(f11423,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4769]) ).
fof(f4769,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(X0)),X0)),
inference(resolution,[],[f4744,f204]) ).
fof(f11673,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11424]) ).
fof(f11424,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4784]) ).
fof(f4784,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(X0))),X0)),
inference(resolution,[],[f4769,f4744]) ).
fof(f11672,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11425]) ).
fof(f11425,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4814]) ).
fof(f4814,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(X0)))),X0)),
inference(resolution,[],[f4784,f4744]) ).
fof(f11671,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11426]) ).
fof(f11426,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4891]) ).
fof(f4891,plain,
! [X0] : is_a_theorem(implies(necessarily(necessarily(necessarily(necessarily(necessarily(X0))))),X0)),
inference(resolution,[],[f4814,f4744]) ).
fof(f11670,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11427]) ).
fof(f11427,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5376]) ).
fof(f5376,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,X1)))),X0)),
inference(resolution,[],[f4730,f4784]) ).
fof(f11669,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11428]) ).
fof(f11428,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5375]) ).
fof(f5375,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,X1))),X0)),
inference(resolution,[],[f4730,f4769]) ).
fof(f11668,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11429]) ).
fof(f11429,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5443]) ).
fof(f5443,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(necessarily(X0),X1))),X0)),
inference(resolution,[],[f5375,f4744]) ).
fof(f11667,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11430]) ).
fof(f11430,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5374]) ).
fof(f5374,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,X1)),X0)),
inference(resolution,[],[f4730,f204]) ).
fof(f11666,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11431]) ).
fof(f11431,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5396]) ).
fof(f5396,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(X0),X1)),X0)),
inference(resolution,[],[f5374,f4744]) ).
fof(f11665,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11432]) ).
fof(f11432,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5456]) ).
fof(f5456,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(necessarily(necessarily(X0)),X1)),X0)),
inference(resolution,[],[f5396,f4744]) ).
fof(f11664,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11433]) ).
fof(f11433,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5393]) ).
fof(f5393,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,X1),X2)),X0)),
inference(resolution,[],[f5374,f4730]) ).
fof(f11663,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11441]) ).
fof(f11441,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5872]) ).
fof(f5872,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,X1)),X1)),
inference(resolution,[],[f4731,f204]) ).
fof(f11662,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11442]) ).
fof(f11442,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5904]) ).
fof(f5904,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(X1))),X1)),
inference(resolution,[],[f5872,f4744]) ).
fof(f11661,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11443]) ).
fof(f11443,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f6009]) ).
fof(f6009,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(and(X0,necessarily(necessarily(X1)))),X1)),
inference(resolution,[],[f5904,f4744]) ).
fof(f11660,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11444]) ).
fof(f11444,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5901]) ).
fof(f5901,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,X2))),X1)),
inference(resolution,[],[f5872,f4730]) ).
fof(f11659,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11445]) ).
fof(f11445,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5880]) ).
fof(f5880,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(and(X0,X1),X2)),X1)),
inference(resolution,[],[f4731,f5374]) ).
fof(f11658,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11446]) ).
fof(f11446,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5873]) ).
fof(f5873,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,X1))),X1)),
inference(resolution,[],[f4731,f4769]) ).
fof(f11657,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11447]) ).
fof(f11447,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5962]) ).
fof(f5962,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(and(X0,necessarily(X1)))),X1)),
inference(resolution,[],[f5873,f4744]) ).
fof(f11656,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11448]) ).
fof(f11448,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5874]) ).
fof(f5874,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(necessarily(necessarily(and(X0,X1)))),X1)),
inference(resolution,[],[f4731,f4784]) ).
fof(f11655,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11449]) ).
fof(f11449,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5900]) ).
fof(f5900,plain,
! [X2,X0,X1] : is_a_theorem(implies(necessarily(and(X0,and(X1,X2))),X2)),
inference(resolution,[],[f5872,f4731]) ).
fof(f11654,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11450]) ).
fof(f11450,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f217]) ).
fof(f11653,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11451]) ).
fof(f11451,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5397]) ).
fof(f5397,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,X1)),implies(X0,X1))),
inference(superposition,[],[f5374,f202]) ).
fof(f11652,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11452]) ).
fof(f11452,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5905]) ).
fof(f5905,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,X1)),implies(X1,X0))),
inference(superposition,[],[f5872,f202]) ).
fof(f11651,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11453]) ).
fof(f11453,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f454]) ).
fof(f454,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(not(X0)),implies(possibly(X0),X1))),
inference(superposition,[],[f207,f259]) ).
fof(f11650,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11454]) ).
fof(f11454,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f445]) ).
fof(f445,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(or(X0,X1)),implies(necessarily(not(X0)),necessarily(X1)))),
inference(superposition,[],[f217,f254]) ).
fof(f11649,plain,
( ~ spl1_9
| ~ spl1_10 ),
inference(avatar_contradiction_clause,[],[f11455]) ).
fof(f11455,plain,
( $false
| ~ spl1_9
| ~ spl1_10 ),
inference(resolution,[],[f10228,f10244]) ).
fof(f10244,plain,
( ! [X0] : is_a_theorem(implies(necessarily(not(X0)),not(necessarily(possibly(X0)))))
| ~ spl1_9 ),
inference(superposition,[],[f10225,f223]) ).
fof(f223,plain,
! [X0] : possibly(necessarily(not(X0))) = not(necessarily(possibly(X0))),
inference(superposition,[],[f199,f199]) ).
fof(f11648,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11457]) ).
fof(f11457,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7935]) ).
fof(f7935,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(X0),and(equiv(X1,X1),X0))),
inference(resolution,[],[f7719,f4768]) ).
fof(f4768,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(implies(necessarily(X0),X1)) ),
inference(resolution,[],[f4744,f444]) ).
fof(f444,plain,
! [X0,X1] :
( is_a_theorem(implies(necessarily(X0),necessarily(X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f217,f220]) ).
fof(f7719,plain,
! [X0,X1] : is_a_theorem(necessarily(implies(X0,and(equiv(X1,X1),X0)))),
inference(resolution,[],[f7219,f212]) ).
fof(f7219,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(equiv(X1,X1),X0))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f7140,f4455]) ).
fof(f4455,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X0) ),
inference(forward_demodulation,[],[f4434,f200]) ).
fof(f4434,plain,
! [X0,X1] :
( ~ is_a_theorem(not(and(X0,not(X1))))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f4378,f272]) ).
fof(f272,plain,
! [X0,X1] :
( is_a_theorem(or(X0,and(X1,not(X0))))
| ~ is_a_theorem(X1) ),
inference(superposition,[],[f227,f254]) ).
fof(f227,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,and(X1,X0)))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f220,f212]) ).
fof(f4378,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f4363,f238]) ).
fof(f238,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f227,f220]) ).
fof(f4363,plain,
! [X0,X1] :
( ~ is_a_theorem(and(not(X1),or(X0,X1)))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f2549,f206]) ).
fof(f2549,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(and(not(X0),or(X1,X0))))
| is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f2515,f856]) ).
fof(f856,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f834,f206]) ).
fof(f834,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(necessarily(X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f444,f220]) ).
fof(f11647,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11458]) ).
fof(f11458,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5673]) ).
fof(f5673,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(not(X0),X1)),or(X0,X1))),
inference(superposition,[],[f5374,f404]) ).
fof(f404,plain,
! [X0,X1] : equiv(not(X0),X1) = and(or(X0,X1),implies(X1,not(X0))),
inference(superposition,[],[f202,f254]) ).
fof(f11646,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11459]) ).
fof(f11459,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f5907]) ).
fof(f5907,plain,
! [X0,X1] : is_a_theorem(implies(necessarily(equiv(X0,not(X1))),or(X1,X0))),
inference(superposition,[],[f5872,f405]) ).
fof(f405,plain,
! [X0,X1] : equiv(X1,not(X0)) = and(implies(X1,not(X0)),or(X0,X1)),
inference(superposition,[],[f202,f254]) ).
fof(f11645,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11461]) ).
fof(f11461,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f205]) ).
fof(f11644,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11463]) ).
fof(f11463,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f536]) ).
fof(f536,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(subsumption_resolution,[],[f534,f498]) ).
fof(f534,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[],[f526,f202]) ).
fof(f526,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f499,f220]) ).
fof(f11643,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11467]) ).
fof(f11467,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2169]) ).
fof(f2169,plain,
! [X0] : is_a_theorem(not(and(not(X0),or(X0,X0)))),
inference(superposition,[],[f499,f257]) ).
fof(f11642,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11468]) ).
fof(f11468,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2172]) ).
fof(f2172,plain,
! [X0,X1] : is_a_theorem(not(and(and(not(X0),not(X1)),or(X0,X1)))),
inference(superposition,[],[f498,f257]) ).
fof(f11641,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11469]) ).
fof(f11469,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2222]) ).
fof(f2222,plain,
! [X2,X0,X1] : is_a_theorem(not(and(and(and(not(X0),not(X1)),X2),or(X0,X1)))),
inference(superposition,[],[f210,f257]) ).
fof(f11640,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11470]) ).
fof(f11470,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2223]) ).
fof(f2223,plain,
! [X2,X0,X1] : is_a_theorem(not(and(and(X0,and(not(X1),not(X2))),or(X1,X2)))),
inference(superposition,[],[f211,f257]) ).
fof(f11639,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11471]) ).
fof(f11471,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2228]) ).
fof(f2228,plain,
! [X0,X1] : is_a_theorem(not(and(necessarily(and(not(X0),not(X1))),or(X0,X1)))),
inference(superposition,[],[f204,f257]) ).
fof(f11638,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11487]) ).
fof(f11487,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7338]) ).
fof(f7338,plain,
! [X0] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
inference(resolution,[],[f7145,f499]) ).
fof(f11637,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11488]) ).
fof(f11488,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7383]) ).
fof(f7383,plain,
! [X0,X1] : is_a_theorem(and(equiv(X0,X0),equiv(X1,X1))),
inference(resolution,[],[f7331,f7145]) ).
fof(f11636,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11497]) ).
fof(f11497,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f270]) ).
fof(f270,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(superposition,[],[f209,f254]) ).
fof(f11635,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11498]) ).
fof(f11498,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f271]) ).
fof(f271,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,and(not(X0),X1)))),
inference(superposition,[],[f212,f254]) ).
fof(f11634,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11501]) ).
fof(f11501,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7141]) ).
fof(f11633,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11502]) ).
fof(f11502,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f511]) ).
fof(f511,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[],[f498,f254]) ).
fof(f11632,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11503]) ).
fof(f11503,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f2239]) ).
fof(f11631,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11507]) ).
fof(f11507,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f528]) ).
fof(f528,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[],[f499,f254]) ).
fof(f11630,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11508]) ).
fof(f11508,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7343]) ).
fof(f7343,plain,
! [X0,X1] : is_a_theorem(or(X0,and(equiv(X1,X1),not(X0)))),
inference(resolution,[],[f7145,f273]) ).
fof(f11629,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11511]) ).
fof(f11511,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f274]) ).
fof(f274,plain,
! [X0,X1] : is_a_theorem(or(X0,or(not(X0),X1))),
inference(superposition,[],[f207,f254]) ).
fof(f11628,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11512]) ).
fof(f11512,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f275]) ).
fof(f275,plain,
! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[],[f208,f254]) ).
fof(f11627,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11513]) ).
fof(f11513,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f359]) ).
fof(f359,plain,
! [X0,X1] : is_a_theorem(or(X1,or(X0,and(not(X1),not(X0))))),
inference(superposition,[],[f271,f254]) ).
fof(f11626,plain,
( ~ spl1_9
| ~ spl1_10 ),
inference(avatar_contradiction_clause,[],[f11520]) ).
fof(f11520,plain,
( $false
| ~ spl1_9
| ~ spl1_10 ),
inference(resolution,[],[f10228,f10247]) ).
fof(f10247,plain,
( ! [X0] : is_a_theorem(or(X0,possibly(not(X0))))
| ~ spl1_9 ),
inference(superposition,[],[f10225,f254]) ).
fof(f11625,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11523]) ).
fof(f11523,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7341]) ).
fof(f7341,plain,
! [X0,X1] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(resolution,[],[f7145,f207]) ).
fof(f11624,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11525]) ).
fof(f11525,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f515]) ).
fof(f515,plain,
! [X0,X1] : is_a_theorem(or(and(X0,not(X1)),implies(X0,X1))),
inference(superposition,[],[f511,f200]) ).
fof(f11623,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11526]) ).
fof(f11526,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f516]) ).
fof(f516,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),not(X1)),or(X0,X1))),
inference(superposition,[],[f511,f201]) ).
fof(f11622,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11527]) ).
fof(f11527,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f740]) ).
fof(f740,plain,
! [X0,X1] : is_a_theorem(or(and(X0,possibly(X1)),implies(X0,necessarily(not(X1))))),
inference(superposition,[],[f511,f239]) ).
fof(f239,plain,
! [X0,X1] : implies(X1,necessarily(not(X0))) = not(and(X1,possibly(X0))),
inference(superposition,[],[f200,f199]) ).
fof(f11621,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11531]) ).
fof(f11531,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f789]) ).
fof(f789,plain,
! [X0,X1] : is_a_theorem(or(necessarily(implies(X0,X1)),necessarily(not(necessarily(implies(X0,X1)))))),
inference(forward_demodulation,[],[f778,f254]) ).
fof(f778,plain,
! [X0,X1] : is_a_theorem(implies(not(necessarily(implies(X0,X1))),necessarily(not(necessarily(implies(X0,X1)))))),
inference(superposition,[],[f205,f241]) ).
fof(f241,plain,
! [X0,X1] : possibly(and(X0,not(X1))) = not(necessarily(implies(X0,X1))),
inference(superposition,[],[f199,f200]) ).
fof(f11620,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11532]) ).
fof(f11532,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f276]) ).
fof(f276,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),implies(X1,possibly(X0)))),
inference(superposition,[],[f270,f199]) ).
fof(f11619,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11533]) ).
fof(f11533,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f280]) ).
fof(f280,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),or(possibly(X0),X1))),
inference(superposition,[],[f274,f199]) ).
fof(f11618,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11534]) ).
fof(f11534,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f283]) ).
fof(f283,plain,
! [X0,X1] : is_a_theorem(or(necessarily(not(X0)),or(X1,possibly(X0)))),
inference(superposition,[],[f275,f199]) ).
fof(f11617,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11535]) ).
fof(f11535,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f1038]) ).
fof(f1038,plain,
! [X0,X1] : is_a_theorem(or(necessarily(or(X0,X1)),necessarily(not(necessarily(or(X0,X1)))))),
inference(forward_demodulation,[],[f1020,f254]) ).
fof(f1020,plain,
! [X0,X1] : is_a_theorem(implies(not(necessarily(or(X0,X1))),necessarily(not(necessarily(or(X0,X1)))))),
inference(superposition,[],[f205,f258]) ).
fof(f258,plain,
! [X0,X1] : possibly(and(not(X0),not(X1))) = not(necessarily(or(X0,X1))),
inference(superposition,[],[f199,f201]) ).
fof(f11616,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11536]) ).
fof(f11536,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f835]) ).
fof(f835,plain,
! [X0] : is_a_theorem(or(necessarily(possibly(X0)),necessarily(not(necessarily(possibly(X0)))))),
inference(forward_demodulation,[],[f246,f254]) ).
fof(f246,plain,
! [X0] : is_a_theorem(implies(not(necessarily(possibly(X0))),necessarily(not(necessarily(possibly(X0)))))),
inference(superposition,[],[f205,f223]) ).
fof(f11615,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11540]) ).
fof(f11540,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4558]) ).
fof(f4558,plain,
! [X0] : is_a_theorem(necessarily(implies(X0,X0))),
inference(resolution,[],[f4554,f940]) ).
fof(f940,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(X0,X1)))
| is_a_theorem(necessarily(implies(X0,X1))) ),
inference(resolution,[],[f856,f214]) ).
fof(f4554,plain,
! [X0] : is_a_theorem(necessarily(equiv(X0,X0))),
inference(subsumption_resolution,[],[f4522,f498]) ).
fof(f4522,plain,
! [X0] :
( is_a_theorem(necessarily(equiv(X0,X0)))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[],[f4455,f520]) ).
fof(f11614,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11551]) ).
fof(f11551,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7718]) ).
fof(f7718,plain,
! [X0,X1] : is_a_theorem(necessarily(implies(X0,equiv(X1,X1)))),
inference(resolution,[],[f7219,f209]) ).
fof(f11613,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11555]) ).
fof(f11555,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7719]) ).
fof(f11612,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11559]) ).
fof(f11559,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4554]) ).
fof(f11611,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11568]) ).
fof(f11568,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7726]) ).
fof(f7726,plain,
! [X0] : is_a_theorem(necessarily(and(equiv(X0,X0),equiv(X0,X0)))),
inference(resolution,[],[f7219,f499]) ).
fof(f11610,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11569]) ).
fof(f11569,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7727]) ).
fof(f7727,plain,
! [X0,X1] : is_a_theorem(necessarily(and(equiv(X0,X0),equiv(X1,X1)))),
inference(resolution,[],[f7219,f7331]) ).
fof(f11609,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11582]) ).
fof(f11582,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7731]) ).
fof(f7731,plain,
! [X0,X1] : is_a_theorem(necessarily(or(X0,equiv(X1,X1)))),
inference(resolution,[],[f7219,f208]) ).
fof(f11608,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11584]) ).
fof(f11584,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f4562]) ).
fof(f4562,plain,
! [X0] : is_a_theorem(necessarily(or(X0,not(X0)))),
inference(resolution,[],[f4554,f941]) ).
fof(f941,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(equiv(not(X0),X1)))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(resolution,[],[f856,f267]) ).
fof(f11607,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[],[f11587]) ).
fof(f11587,plain,
( $false
| ~ spl1_10 ),
inference(resolution,[],[f10228,f7730]) ).
fof(f7730,plain,
! [X0,X1] : is_a_theorem(necessarily(or(equiv(X0,X0),X1))),
inference(resolution,[],[f7219,f207]) ).
fof(f11606,plain,
( ~ spl1_9
| ~ spl1_10 ),
inference(avatar_contradiction_clause,[],[f11594]) ).
fof(f11594,plain,
( $false
| ~ spl1_9
| ~ spl1_10 ),
inference(resolution,[],[f10228,f10241]) ).
fof(f10241,plain,
( ! [X0] : is_a_theorem(necessarily(possibly(equiv(X0,X0))))
| ~ spl1_9 ),
inference(resolution,[],[f10225,f7219]) ).
fof(f11605,plain,
( ~ spl1_9
| ~ spl1_10 ),
inference(avatar_contradiction_clause,[],[f11598]) ).
fof(f11598,plain,
( $false
| ~ spl1_9
| ~ spl1_10 ),
inference(resolution,[],[f10228,f10243]) ).
fof(f10243,plain,
( ! [X0] : is_a_theorem(possibly(equiv(X0,X0)))
| ~ spl1_9 ),
inference(resolution,[],[f10225,f7145]) ).
fof(f11306,plain,
( spl1_10
| spl1_11
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f11231,f10224,f11304,f10227]) ).
fof(f11304,plain,
( spl1_11
<=> ! [X0] : is_a_theorem(possibly(possibly(equiv(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f11231,plain,
( ! [X0,X1] :
( is_a_theorem(possibly(possibly(equiv(X0,X0))))
| ~ is_a_theorem(X1) )
| ~ spl1_9 ),
inference(resolution,[],[f11083,f10214]) ).
fof(f10214,plain,
! [X0,X1] :
( is_a_theorem(and(X0,possibly(equiv(X1,X1))))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f10188,f7145]) ).
fof(f10188,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,and(X1,possibly(X0))))
| ~ is_a_theorem(X1) ),
inference(forward_demodulation,[],[f10162,f199]) ).
fof(f10162,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,and(X1,not(necessarily(not(X0))))))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f1159,f4761]) ).
fof(f4761,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,necessarily(X1)),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f4744,f4601]) ).
fof(f11083,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X1,X0))
| is_a_theorem(possibly(X0)) )
| ~ spl1_9 ),
inference(resolution,[],[f10669,f211]) ).
fof(f10669,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(possibly(X1))
| ~ is_a_theorem(X0) )
| ~ spl1_9 ),
inference(resolution,[],[f10235,f220]) ).
fof(f10235,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,possibly(X1)))
| ~ is_a_theorem(implies(X0,X1)) )
| ~ spl1_9 ),
inference(resolution,[],[f10225,f1390]) ).
fof(f10229,plain,
( spl1_9
| spl1_10 ),
inference(avatar_split_clause,[],[f10199,f10227,f10224]) ).
fof(f10199,plain,
! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,possibly(X1))) ),
inference(resolution,[],[f10188,f4731]) ).
fof(f7997,plain,
( spl1_8
| spl1_2 ),
inference(avatar_split_clause,[],[f7668,f296,f7995]) ).
fof(f7995,plain,
( spl1_8
<=> ! [X1] : ~ is_a_theorem(not(not(not(equiv(X1,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f296,plain,
( spl1_2
<=> ! [X0] : is_a_theorem(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f7668,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(not(not(equiv(X1,X1))))) ),
inference(resolution,[],[f7216,f3895]) ).
fof(f3895,plain,
! [X0,X1] :
( is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(not(not(not(X0)))) ),
inference(resolution,[],[f3865,f946]) ).
fof(f946,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(or(X0,not(X1))))
| is_a_theorem(necessarily(implies(X1,X0))) ),
inference(resolution,[],[f856,f291]) ).
fof(f3865,plain,
! [X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(not(not(X1))) ),
inference(superposition,[],[f3839,f254]) ).
fof(f3839,plain,
! [X0,X1] :
( is_a_theorem(necessarily(implies(X1,X0)))
| ~ is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f3826,f946]) ).
fof(f3826,plain,
! [X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(not(not(X0))) ),
inference(resolution,[],[f3816,f206]) ).
fof(f3816,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(not(not(X0))))
| is_a_theorem(necessarily(or(X0,X1))) ),
inference(superposition,[],[f3798,f254]) ).
fof(f3798,plain,
! [X0,X1] :
( is_a_theorem(necessarily(implies(X0,X1)))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(resolution,[],[f946,f931]) ).
fof(f931,plain,
! [X0,X1] :
( is_a_theorem(necessarily(or(X1,X0)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f856,f208]) ).
fof(f7216,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(equiv(X1,X1),X0)))
| is_a_theorem(X0) ),
inference(resolution,[],[f7140,f993]) ).
fof(f993,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f991,f644]) ).
fof(f991,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f930,f232]) ).
fof(f232,plain,
! [X0] :
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(resolution,[],[f220,f204]) ).
fof(f930,plain,
! [X0,X1] :
( is_a_theorem(necessarily(or(X0,X1)))
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[],[f856,f207]) ).
fof(f7685,plain,
( spl1_7
| spl1_2 ),
inference(avatar_split_clause,[],[f7665,f296,f7683]) ).
fof(f7683,plain,
( spl1_7
<=> ! [X1] : ~ is_a_theorem(necessarily(not(equiv(X1,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f7665,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(not(equiv(X1,X1)))) ),
inference(resolution,[],[f7216,f3798]) ).
fof(f5281,plain,
( spl1_6
| spl1_2 ),
inference(avatar_split_clause,[],[f5149,f296,f5279]) ).
fof(f5279,plain,
( spl1_6
<=> ! [X1] :
( ~ is_a_theorem(X1)
| ~ is_a_theorem(not(not(not(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f5149,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(not(not(not(X1)))) ),
inference(resolution,[],[f4662,f3895]) ).
fof(f4662,plain,
! [X0,X1] :
( ~ is_a_theorem(necessarily(implies(X0,X1)))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f4601,f993]) ).
fof(f3967,plain,
( spl1_4
| spl1_5 ),
inference(avatar_split_clause,[],[f3862,f3965,f3962]) ).
fof(f3962,plain,
( spl1_4
<=> ! [X1] : ~ is_a_theorem(necessarily(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f3965,plain,
( spl1_5
<=> ! [X0] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(necessarily(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f3862,plain,
! [X0,X1] :
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(necessarily(X1)) ),
inference(resolution,[],[f3839,f834]) ).
fof(f1397,plain,
( spl1_3
| spl1_2 ),
inference(avatar_split_clause,[],[f1246,f296,f1395]) ).
fof(f1395,plain,
( spl1_3
<=> ! [X1] :
( ~ is_a_theorem(necessarily(possibly(X1)))
| ~ is_a_theorem(necessarily(not(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f1246,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(possibly(X1)))
| ~ is_a_theorem(necessarily(not(X1))) ),
inference(resolution,[],[f993,f456]) ).
fof(f456,plain,
! [X0,X1] :
( is_a_theorem(implies(possibly(X0),X1))
| ~ is_a_theorem(necessarily(not(X0))) ),
inference(superposition,[],[f224,f259]) ).
fof(f224,plain,
! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[],[f220,f207]) ).
fof(f312,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f299]) ).
fof(f299,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f297,f203]) ).
fof(f297,plain,
( ! [X0] : is_a_theorem(X0)
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f311,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f308]) ).
fof(f308,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f297,f235]) ).
fof(f235,plain,
~ is_a_theorem(necessarily(possibly(sK0))),
inference(resolution,[],[f226,f203]) ).
fof(f310,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f309,plain,
( $false
| ~ spl1_2 ),
inference(resolution,[],[f297,f237]) ).
fof(f237,plain,
~ is_a_theorem(possibly(sK0)),
inference(resolution,[],[f235,f206]) ).
fof(f298,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f287,f296,f293]) ).
fof(f293,plain,
( spl1_1
<=> ! [X1] :
( ~ is_a_theorem(not(X1))
| ~ is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f287,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(X1))
| ~ is_a_theorem(X1) ),
inference(resolution,[],[f266,f224]) ).
fof(f266,plain,
! [X0,X1] :
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[],[f220,f254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL524+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 13:21:56 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (6600)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (6603)WARNING: value z3 for option sas not known
% 0.20/0.38 % (6602)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38 % (6604)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38 % (6601)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38 % (6606)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)
% 0.20/0.38 % (6603)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)
% 0.20/0.38 % (6605)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)
% 0.20/0.38 % (6607)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)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.39 TRYING [1]
% 0.20/0.39 TRYING [3]
% 0.20/0.39 TRYING [2]
% 0.20/0.40 TRYING [4]
% 0.20/0.40 TRYING [3]
% 0.20/0.46 TRYING [4]
% 0.20/0.47 TRYING [5]
% 0.20/0.51 TRYING [1]
% 0.20/0.51 TRYING [2]
% 0.20/0.51 TRYING [3]
% 0.20/0.52 TRYING [4]
% 1.44/0.58 TRYING [5]
% 1.44/0.60 TRYING [5]
% 1.97/0.66 TRYING [6]
% 3.33/0.85 TRYING [6]
% 7.13/1.42 TRYING [7]
% 13.34/2.30 TRYING [7]
% 16.16/2.69 TRYING [6]
% 98.68/14.49 TRYING [8]
% 111.75/16.37 TRYING [8]
% 221.25/32.01 % (6603)First to succeed.
% 221.25/32.02 % (6603)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6600"
% 221.25/32.03 % (6603)Refutation found. Thanks to Tanya!
% 221.25/32.03 % SZS status Theorem for theBenchmark
% 221.25/32.03 % SZS output start Proof for theBenchmark
% See solution above
% 221.25/32.04 % (6603)------------------------------
% 221.25/32.04 % (6603)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 221.25/32.04 % (6603)Termination reason: Refutation
% 221.25/32.04
% 221.25/32.04 % (6603)Memory used [KB]: 89402
% 221.25/32.04 % (6603)Time elapsed: 31.647 s
% 221.25/32.04 % (6603)Instructions burned: 107644 (million)
% 221.25/32.04 % (6600)Success in time 31.579 s
%------------------------------------------------------------------------------