TSTP Solution File: LCL456+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL456+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:42:26 EDT 2024
% Result : Theorem 0.16s 0.42s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 135
% Syntax : Number of formulae : 408 ( 66 unt; 0 def)
% Number of atoms : 929 ( 71 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 911 ( 390 ~; 385 |; 2 &)
% ( 109 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 117 ( 115 usr; 115 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 527 ( 523 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1846,plain,
$false,
inference(avatar_sat_refutation,[],[f154,f159,f164,f169,f174,f179,f184,f189,f194,f199,f204,f209,f214,f219,f224,f229,f234,f239,f244,f249,f254,f258,f262,f266,f270,f274,f278,f282,f288,f293,f297,f301,f305,f309,f321,f325,f331,f336,f344,f362,f367,f378,f382,f387,f394,f399,f406,f410,f414,f432,f436,f440,f444,f449,f493,f507,f511,f515,f519,f525,f529,f710,f714,f719,f723,f727,f731,f735,f739,f743,f747,f868,f1111,f1115,f1119,f1123,f1127,f1131,f1511,f1562,f1578,f1582,f1586,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1817,f1821,f1825,f1840]) ).
fof(f1840,plain,
( spl2_30
| ~ spl2_92 ),
inference(avatar_contradiction_clause,[],[f1830]) ).
fof(f1830,plain,
( $false
| spl2_30
| ~ spl2_92 ),
inference(resolution,[],[f1820,f292]) ).
fof(f292,plain,
( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
| spl2_30 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f290,plain,
( spl2_30
<=> is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
fof(f1820,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X1,X0),or(X0,X1)))
| ~ spl2_92 ),
inference(avatar_component_clause,[],[f1819]) ).
fof(f1819,plain,
( spl2_92
<=> ! [X0,X1] : is_a_theorem(implies(or(X1,X0),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_92])]) ).
fof(f1825,plain,
( spl2_93
| ~ spl2_55
| ~ spl2_60 ),
inference(avatar_split_clause,[],[f671,f523,f491,f1823]) ).
fof(f1823,plain,
( spl2_93
<=> ! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_93])]) ).
fof(f491,plain,
( spl2_55
<=> ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_55])]) ).
fof(f523,plain,
( spl2_60
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_60])]) ).
fof(f671,plain,
( ! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0)))
| ~ spl2_55
| ~ spl2_60 ),
inference(resolution,[],[f524,f492]) ).
fof(f492,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_55 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f524,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ spl2_60 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f1821,plain,
( spl2_92
| ~ spl2_36
| ~ spl2_39
| ~ spl2_41
| ~ spl2_53 ),
inference(avatar_split_clause,[],[f482,f442,f365,f342,f323,f1819]) ).
fof(f323,plain,
( spl2_36
<=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
fof(f342,plain,
( spl2_39
<=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).
fof(f365,plain,
( spl2_41
<=> ! [X0,X1] : is_a_theorem(or(and(not(X1),X0),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
fof(f442,plain,
( spl2_53
<=> ! [X0,X1] : or(X0,X1) = implies(not(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_53])]) ).
fof(f482,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X1,X0),or(X0,X1)))
| ~ spl2_36
| ~ spl2_39
| ~ spl2_41
| ~ spl2_53 ),
inference(forward_demodulation,[],[f481,f443]) ).
fof(f443,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl2_53 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f481,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),X0),or(X0,X1)))
| ~ spl2_36
| ~ spl2_39
| ~ spl2_41
| ~ spl2_53 ),
inference(forward_demodulation,[],[f461,f356]) ).
fof(f356,plain,
( ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2)
| ~ spl2_36
| ~ spl2_39 ),
inference(forward_demodulation,[],[f345,f324]) ).
fof(f324,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ spl2_36 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f345,plain,
( ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = not(and(implies(X0,X1),not(X2)))
| ~ spl2_36
| ~ spl2_39 ),
inference(superposition,[],[f343,f324]) ).
fof(f343,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f461,plain,
( ! [X0,X1] : is_a_theorem(or(and(not(X1),not(X0)),or(X0,X1)))
| ~ spl2_41
| ~ spl2_53 ),
inference(superposition,[],[f366,f443]) ).
fof(f366,plain,
( ! [X0,X1] : is_a_theorem(or(and(not(X1),X0),implies(X0,X1)))
| ~ spl2_41 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f1817,plain,
( spl2_91
| ~ spl2_34
| ~ spl2_50 ),
inference(avatar_split_clause,[],[f450,f430,f307,f1815]) ).
fof(f1815,plain,
( spl2_91
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_91])]) ).
fof(f307,plain,
( spl2_34
<=> ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
fof(f430,plain,
( spl2_50
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_50])]) ).
fof(f450,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) )
| ~ spl2_34
| ~ spl2_50 ),
inference(resolution,[],[f431,f308]) ).
fof(f308,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) )
| ~ spl2_34 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f431,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) )
| ~ spl2_50 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f1663,plain,
( spl2_90
| ~ spl2_26
| ~ spl2_67 ),
inference(avatar_split_clause,[],[f984,f729,f272,f1661]) ).
fof(f1661,plain,
( spl2_90
<=> ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_90])]) ).
fof(f272,plain,
( spl2_26
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
fof(f729,plain,
( spl2_67
<=> ! [X2,X0,X1] : implies(and(not(X0),not(X1)),X2) = or(or(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_67])]) ).
fof(f984,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X1)))
| ~ spl2_26
| ~ spl2_67 ),
inference(superposition,[],[f273,f730]) ).
fof(f730,plain,
( ! [X2,X0,X1] : implies(and(not(X0),not(X1)),X2) = or(or(X0,X1),X2)
| ~ spl2_67 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f273,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f1659,plain,
( spl2_89
| ~ spl2_25
| ~ spl2_67 ),
inference(avatar_split_clause,[],[f983,f729,f268,f1657]) ).
fof(f1657,plain,
( spl2_89
<=> ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_89])]) ).
fof(f268,plain,
( spl2_25
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
fof(f983,plain,
( ! [X0,X1] : is_a_theorem(or(or(X0,X1),not(X0)))
| ~ spl2_25
| ~ spl2_67 ),
inference(superposition,[],[f269,f730]) ).
fof(f269,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ spl2_25 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f1655,plain,
( spl2_88
| ~ spl2_26
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f534,f505,f272,f1653]) ).
fof(f1653,plain,
( spl2_88
<=> ! [X0,X1] : is_a_theorem(or(implies(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_88])]) ).
fof(f505,plain,
( spl2_56
<=> ! [X2,X0,X1] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_56])]) ).
fof(f534,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),not(X1)))
| ~ spl2_26
| ~ spl2_56 ),
inference(superposition,[],[f273,f506]) ).
fof(f506,plain,
( ! [X2,X0,X1] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2)
| ~ spl2_56 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f1651,plain,
( spl2_87
| ~ spl2_23
| ~ spl2_53 ),
inference(avatar_split_clause,[],[f478,f442,f260,f1649]) ).
fof(f1649,plain,
( spl2_87
<=> ! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_87])]) ).
fof(f260,plain,
( spl2_23
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
fof(f478,plain,
( ! [X0,X1] : is_a_theorem(or(X0,or(X1,not(X0))))
| ~ spl2_23
| ~ spl2_53 ),
inference(superposition,[],[f261,f443]) ).
fof(f261,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f1647,plain,
( spl2_86
| ~ spl2_53
| ~ spl2_80 ),
inference(avatar_split_clause,[],[f1568,f1560,f442,f1645]) ).
fof(f1645,plain,
( spl2_86
<=> ! [X0] : is_a_theorem(or(X0,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_86])]) ).
fof(f1560,plain,
( spl2_80
<=> ! [X0] : is_a_theorem(implies(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_80])]) ).
fof(f1568,plain,
( ! [X0] : is_a_theorem(or(X0,not(X0)))
| ~ spl2_53
| ~ spl2_80 ),
inference(superposition,[],[f1561,f443]) ).
fof(f1561,plain,
( ! [X0] : is_a_theorem(implies(X0,X0))
| ~ spl2_80 ),
inference(avatar_component_clause,[],[f1560]) ).
fof(f1643,plain,
( spl2_85
| ~ spl2_24
| ~ spl2_53 ),
inference(avatar_split_clause,[],[f471,f442,f264,f1641]) ).
fof(f1641,plain,
( spl2_85
<=> ! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_85])]) ).
fof(f264,plain,
( spl2_24
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
fof(f471,plain,
( ! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0))))
| ~ spl2_24
| ~ spl2_53 ),
inference(superposition,[],[f265,f443]) ).
fof(f265,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ spl2_24 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f1639,plain,
( spl2_84
| ~ spl2_28
| ~ spl2_35 ),
inference(avatar_split_clause,[],[f415,f319,f280,f1637]) ).
fof(f1637,plain,
( spl2_84
<=> ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_84])]) ).
fof(f280,plain,
( spl2_28
<=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
fof(f319,plain,
( spl2_35
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
fof(f415,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(X0)) )
| ~ spl2_28
| ~ spl2_35 ),
inference(superposition,[],[f320,f281]) ).
fof(f281,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f320,plain,
( ! [X0,X1] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X0) )
| ~ spl2_35 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f1586,plain,
( spl2_83
| ~ spl2_25
| ~ spl2_56 ),
inference(avatar_split_clause,[],[f533,f505,f268,f1584]) ).
fof(f1584,plain,
( spl2_83
<=> ! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_83])]) ).
fof(f533,plain,
( ! [X0,X1] : is_a_theorem(or(implies(X0,X1),X0))
| ~ spl2_25
| ~ spl2_56 ),
inference(superposition,[],[f269,f506]) ).
fof(f1582,plain,
( spl2_82
| ~ spl2_31
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f495,f491,f295,f1580]) ).
fof(f1580,plain,
( spl2_82
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_82])]) ).
fof(f295,plain,
( spl2_31
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
fof(f495,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ spl2_31
| ~ spl2_55 ),
inference(resolution,[],[f492,f296]) ).
fof(f296,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ spl2_31 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f1578,plain,
( spl2_81
| ~ spl2_29
| ~ spl2_53 ),
inference(avatar_split_clause,[],[f455,f442,f286,f1576]) ).
fof(f1576,plain,
( spl2_81
<=> ! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_81])]) ).
fof(f286,plain,
( spl2_29
<=> ! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
fof(f455,plain,
( ! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1)))
| ~ spl2_29
| ~ spl2_53 ),
inference(superposition,[],[f287,f443]) ).
fof(f287,plain,
( ! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1)))
| ~ spl2_29 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f1562,plain,
( spl2_80
| ~ spl2_24
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f494,f491,f264,f1560]) ).
fof(f494,plain,
( ! [X0] : is_a_theorem(implies(X0,X0))
| ~ spl2_24
| ~ spl2_55 ),
inference(resolution,[],[f492,f265]) ).
fof(f1511,plain,
( spl2_79
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f349,f342,f1509]) ).
fof(f1509,plain,
( spl2_79
<=> ! [X2,X0,X1] : or(X2,and(not(X0),not(X1))) = not(and(not(X2),or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_79])]) ).
fof(f349,plain,
( ! [X2,X0,X1] : or(X2,and(not(X0),not(X1))) = not(and(not(X2),or(X0,X1)))
| ~ spl2_39 ),
inference(superposition,[],[f343,f343]) ).
fof(f1131,plain,
( spl2_78
| ~ spl2_28
| ~ spl2_36
| ~ spl2_39
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f402,f397,f342,f323,f280,f1129]) ).
fof(f1129,plain,
( spl2_78
<=> ! [X2,X0,X1] : is_a_theorem(implies(or(X0,X2),implies(implies(X1,X2),implies(implies(X0,X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_78])]) ).
fof(f397,plain,
( spl2_46
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_46])]) ).
fof(f402,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(or(X0,X2),implies(implies(X1,X2),implies(implies(X0,X1),X2))))
| ~ spl2_28
| ~ spl2_36
| ~ spl2_39
| ~ spl2_46 ),
inference(forward_demodulation,[],[f401,f351]) ).
fof(f351,plain,
( ! [X0,X1] : or(X0,X1) = implies(not(X0),X1)
| ~ spl2_36
| ~ spl2_39 ),
inference(superposition,[],[f343,f324]) ).
fof(f401,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(not(X0),X2),implies(implies(X1,X2),implies(implies(X0,X1),X2))))
| ~ spl2_28
| ~ spl2_46 ),
inference(superposition,[],[f398,f281]) ).
fof(f398,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
| ~ spl2_46 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f1127,plain,
( spl2_77
| ~ spl2_34
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f400,f397,f307,f1125]) ).
fof(f1125,plain,
( spl2_77
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_77])]) ).
fof(f400,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1))) )
| ~ spl2_34
| ~ spl2_46 ),
inference(resolution,[],[f398,f308]) ).
fof(f1123,plain,
( spl2_76
| ~ spl2_36
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f354,f342,f323,f1121]) ).
fof(f1121,plain,
( spl2_76
<=> ! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_76])]) ).
fof(f354,plain,
( ! [X2,X0,X1] : implies(X2,and(not(X0),not(X1))) = not(and(X2,or(X0,X1)))
| ~ spl2_36
| ~ spl2_39 ),
inference(superposition,[],[f324,f343]) ).
fof(f1119,plain,
( spl2_75
| ~ spl2_38
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f353,f342,f334,f1117]) ).
fof(f1117,plain,
( spl2_75
<=> ! [X2,X0,X1] : and(X2,and(not(X0),not(X1))) = not(implies(X2,or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_75])]) ).
fof(f334,plain,
( spl2_38
<=> ! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
fof(f353,plain,
( ! [X2,X0,X1] : and(X2,and(not(X0),not(X1))) = not(implies(X2,or(X0,X1)))
| ~ spl2_38
| ~ spl2_39 ),
inference(superposition,[],[f335,f343]) ).
fof(f335,plain,
( ! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1)))
| ~ spl2_38 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f1115,plain,
( spl2_74
| ~ spl2_38
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f350,f342,f334,f1113]) ).
fof(f1113,plain,
( spl2_74
<=> ! [X2,X0,X1] : or(X2,implies(X0,not(X1))) = not(and(not(X2),and(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_74])]) ).
fof(f350,plain,
( ! [X2,X0,X1] : or(X2,implies(X0,not(X1))) = not(and(not(X2),and(X0,X1)))
| ~ spl2_38
| ~ spl2_39 ),
inference(superposition,[],[f343,f335]) ).
fof(f1111,plain,
( spl2_73
| ~ spl2_36
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f348,f342,f323,f1109]) ).
fof(f1109,plain,
( spl2_73
<=> ! [X2,X0,X1] : or(X2,and(X0,not(X1))) = not(and(not(X2),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_73])]) ).
fof(f348,plain,
( ! [X2,X0,X1] : or(X2,and(X0,not(X1))) = not(and(not(X2),implies(X0,X1)))
| ~ spl2_36
| ~ spl2_39 ),
inference(superposition,[],[f343,f324]) ).
fof(f868,plain,
( ~ spl2_72
| ~ spl2_35
| spl2_54 ),
inference(avatar_split_clause,[],[f521,f446,f319,f865]) ).
fof(f865,plain,
( spl2_72
<=> is_a_theorem(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_72])]) ).
fof(f446,plain,
( spl2_54
<=> is_a_theorem(or(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_54])]) ).
fof(f521,plain,
( ~ is_a_theorem(sK1)
| ~ spl2_35
| spl2_54 ),
inference(resolution,[],[f448,f320]) ).
fof(f448,plain,
( ~ is_a_theorem(or(sK1,sK0))
| spl2_54 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f747,plain,
( spl2_71
| ~ spl2_36
| ~ spl2_38
| ~ spl2_41 ),
inference(avatar_split_clause,[],[f374,f365,f334,f323,f745]) ).
fof(f745,plain,
( spl2_71
<=> ! [X2,X0,X1] : is_a_theorem(or(and(and(X0,X1),X2),not(and(X2,and(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_71])]) ).
fof(f374,plain,
( ! [X2,X0,X1] : is_a_theorem(or(and(and(X0,X1),X2),not(and(X2,and(X0,X1)))))
| ~ spl2_36
| ~ spl2_38
| ~ spl2_41 ),
inference(forward_demodulation,[],[f370,f339]) ).
fof(f339,plain,
( ! [X2,X0,X1] : implies(X2,implies(X0,not(X1))) = not(and(X2,and(X0,X1)))
| ~ spl2_36
| ~ spl2_38 ),
inference(superposition,[],[f324,f335]) ).
fof(f370,plain,
( ! [X2,X0,X1] : is_a_theorem(or(and(and(X0,X1),X2),implies(X2,implies(X0,not(X1)))))
| ~ spl2_38
| ~ spl2_41 ),
inference(superposition,[],[f366,f335]) ).
fof(f743,plain,
( spl2_70
| ~ spl2_36
| ~ spl2_39
| ~ spl2_41 ),
inference(avatar_split_clause,[],[f373,f365,f342,f323,f741]) ).
fof(f741,plain,
( spl2_70
<=> ! [X2,X0,X1] : is_a_theorem(or(and(or(X0,X1),X2),not(and(X2,or(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_70])]) ).
fof(f373,plain,
( ! [X2,X0,X1] : is_a_theorem(or(and(or(X0,X1),X2),not(and(X2,or(X0,X1)))))
| ~ spl2_36
| ~ spl2_39
| ~ spl2_41 ),
inference(forward_demodulation,[],[f372,f351]) ).
fof(f372,plain,
( ! [X2,X0,X1] : is_a_theorem(or(and(or(X0,X1),X2),not(and(X2,implies(not(X0),X1)))))
| ~ spl2_36
| ~ spl2_39
| ~ spl2_41 ),
inference(forward_demodulation,[],[f369,f326]) ).
fof(f326,plain,
( ! [X2,X0,X1] : implies(X2,and(X0,not(X1))) = not(and(X2,implies(X0,X1)))
| ~ spl2_36 ),
inference(superposition,[],[f324,f324]) ).
fof(f369,plain,
( ! [X2,X0,X1] : is_a_theorem(or(and(or(X0,X1),X2),implies(X2,and(not(X0),not(X1)))))
| ~ spl2_39
| ~ spl2_41 ),
inference(superposition,[],[f366,f343]) ).
fof(f739,plain,
( spl2_69
| ~ spl2_36
| ~ spl2_41 ),
inference(avatar_split_clause,[],[f371,f365,f323,f737]) ).
fof(f737,plain,
( spl2_69
<=> ! [X2,X0,X1] : is_a_theorem(or(and(implies(X0,X1),X2),not(and(X2,implies(X0,X1))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_69])]) ).
fof(f371,plain,
( ! [X2,X0,X1] : is_a_theorem(or(and(implies(X0,X1),X2),not(and(X2,implies(X0,X1)))))
| ~ spl2_36
| ~ spl2_41 ),
inference(forward_demodulation,[],[f368,f326]) ).
fof(f368,plain,
( ! [X2,X0,X1] : is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,and(X0,not(X1)))))
| ~ spl2_36
| ~ spl2_41 ),
inference(superposition,[],[f366,f324]) ).
fof(f735,plain,
( spl2_68
| ~ spl2_36
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f357,f342,f323,f733]) ).
fof(f733,plain,
( spl2_68
<=> ! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_68])]) ).
fof(f357,plain,
( ! [X2,X0,X1] : implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2)
| ~ spl2_36
| ~ spl2_39 ),
inference(forward_demodulation,[],[f346,f324]) ).
fof(f346,plain,
( ! [X2,X0,X1] : or(and(not(X0),not(X1)),X2) = not(and(or(X0,X1),not(X2)))
| ~ spl2_39 ),
inference(superposition,[],[f343,f343]) ).
fof(f731,plain,
( spl2_67
| ~ spl2_28
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f355,f342,f280,f729]) ).
fof(f355,plain,
( ! [X2,X0,X1] : implies(and(not(X0),not(X1)),X2) = or(or(X0,X1),X2)
| ~ spl2_28
| ~ spl2_39 ),
inference(superposition,[],[f281,f343]) ).
fof(f727,plain,
( spl2_66
| ~ spl2_36
| ~ spl2_38 ),
inference(avatar_split_clause,[],[f339,f334,f323,f725]) ).
fof(f725,plain,
( spl2_66
<=> ! [X2,X0,X1] : implies(X2,implies(X0,not(X1))) = not(and(X2,and(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_66])]) ).
fof(f723,plain,
( spl2_65
| ~ spl2_38 ),
inference(avatar_split_clause,[],[f338,f334,f721]) ).
fof(f721,plain,
( spl2_65
<=> ! [X2,X0,X1] : and(X2,implies(X0,not(X1))) = not(implies(X2,and(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_65])]) ).
fof(f338,plain,
( ! [X2,X0,X1] : and(X2,implies(X0,not(X1))) = not(implies(X2,and(X0,X1)))
| ~ spl2_38 ),
inference(superposition,[],[f335,f335]) ).
fof(f719,plain,
( ~ spl2_64
| ~ spl2_42
| spl2_54 ),
inference(avatar_split_clause,[],[f520,f446,f376,f716]) ).
fof(f716,plain,
( spl2_64
<=> is_a_theorem(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_64])]) ).
fof(f376,plain,
( spl2_42
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).
fof(f520,plain,
( ~ is_a_theorem(sK0)
| ~ spl2_42
| spl2_54 ),
inference(resolution,[],[f448,f377]) ).
fof(f377,plain,
( ! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(X0) )
| ~ spl2_42 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f714,plain,
( spl2_63
| ~ spl2_36
| ~ spl2_38 ),
inference(avatar_split_clause,[],[f337,f334,f323,f712]) ).
fof(f712,plain,
( spl2_63
<=> ! [X2,X0,X1] : and(X2,and(X0,not(X1))) = not(implies(X2,implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_63])]) ).
fof(f337,plain,
( ! [X2,X0,X1] : and(X2,and(X0,not(X1))) = not(implies(X2,implies(X0,X1)))
| ~ spl2_36
| ~ spl2_38 ),
inference(superposition,[],[f335,f324]) ).
fof(f710,plain,
( spl2_62
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f326,f323,f708]) ).
fof(f708,plain,
( spl2_62
<=> ! [X2,X0,X1] : implies(X2,and(X0,not(X1))) = not(and(X2,implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_62])]) ).
fof(f529,plain,
( spl2_61
| ~ spl2_34
| ~ spl2_45 ),
inference(avatar_split_clause,[],[f395,f392,f307,f527]) ).
fof(f527,plain,
( spl2_61
<=> ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_61])]) ).
fof(f392,plain,
( spl2_45
<=> ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_45])]) ).
fof(f395,plain,
( ! [X2,X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X0,X2))) )
| ~ spl2_34
| ~ spl2_45 ),
inference(resolution,[],[f393,f308]) ).
fof(f393,plain,
( ! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ spl2_45 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f525,plain,
( spl2_60
| ~ spl2_31
| ~ spl2_44 ),
inference(avatar_split_clause,[],[f388,f385,f295,f523]) ).
fof(f385,plain,
( spl2_44
<=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_44])]) ).
fof(f388,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ spl2_31
| ~ spl2_44 ),
inference(superposition,[],[f296,f386]) ).
fof(f386,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ spl2_44 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f519,plain,
( spl2_59
| ~ spl2_36
| ~ spl2_38
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f358,f342,f334,f323,f517]) ).
fof(f517,plain,
( spl2_59
<=> ! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_59])]) ).
fof(f358,plain,
( ! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2)
| ~ spl2_36
| ~ spl2_38
| ~ spl2_39 ),
inference(forward_demodulation,[],[f347,f324]) ).
fof(f347,plain,
( ! [X2,X0,X1] : or(implies(X0,not(X1)),X2) = not(and(and(X0,X1),not(X2)))
| ~ spl2_38
| ~ spl2_39 ),
inference(superposition,[],[f343,f335]) ).
fof(f515,plain,
( spl2_58
| ~ spl2_36
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f356,f342,f323,f513]) ).
fof(f513,plain,
( spl2_58
<=> ! [X2,X0,X1] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_58])]) ).
fof(f511,plain,
( spl2_57
| ~ spl2_28
| ~ spl2_38 ),
inference(avatar_split_clause,[],[f340,f334,f280,f509]) ).
fof(f509,plain,
( spl2_57
<=> ! [X2,X0,X1] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_57])]) ).
fof(f340,plain,
( ! [X2,X0,X1] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2)
| ~ spl2_28
| ~ spl2_38 ),
inference(superposition,[],[f281,f335]) ).
fof(f507,plain,
( spl2_56
| ~ spl2_28
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f327,f323,f280,f505]) ).
fof(f327,plain,
( ! [X2,X0,X1] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2)
| ~ spl2_28
| ~ spl2_36 ),
inference(superposition,[],[f281,f324]) ).
fof(f493,plain,
( spl2_55
| ~ spl2_34
| ~ spl2_43 ),
inference(avatar_split_clause,[],[f383,f380,f307,f491]) ).
fof(f380,plain,
( spl2_43
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
fof(f383,plain,
( ! [X0,X1] :
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_34
| ~ spl2_43 ),
inference(resolution,[],[f381,f308]) ).
fof(f381,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ spl2_43 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f449,plain,
( ~ spl2_54
| spl2_30
| ~ spl2_47 ),
inference(avatar_split_clause,[],[f417,f404,f290,f446]) ).
fof(f404,plain,
( spl2_47
<=> ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_47])]) ).
fof(f417,plain,
( ~ is_a_theorem(or(sK1,sK0))
| spl2_30
| ~ spl2_47 ),
inference(resolution,[],[f405,f292]) ).
fof(f405,plain,
( ! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) )
| ~ spl2_47 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f444,plain,
( spl2_53
| ~ spl2_36
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f351,f342,f323,f442]) ).
fof(f440,plain,
( spl2_52
| ~ spl2_33
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f317,f307,f303,f438]) ).
fof(f438,plain,
( spl2_52
<=> ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_52])]) ).
fof(f303,plain,
( spl2_33
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
fof(f317,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) )
| ~ spl2_33
| ~ spl2_34 ),
inference(resolution,[],[f308,f304]) ).
fof(f304,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ spl2_33 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f436,plain,
( spl2_51
| ~ spl2_32
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f316,f307,f299,f434]) ).
fof(f434,plain,
( spl2_51
<=> ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_51])]) ).
fof(f299,plain,
( spl2_32
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
fof(f316,plain,
( ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X1,X0)) )
| ~ spl2_32
| ~ spl2_34 ),
inference(resolution,[],[f308,f300]) ).
fof(f300,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f432,plain,
( spl2_50
| ~ spl2_31
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f313,f307,f295,f430]) ).
fof(f313,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,and(X0,X1))) )
| ~ spl2_31
| ~ spl2_34 ),
inference(resolution,[],[f308,f296]) ).
fof(f414,plain,
( spl2_49
| ~ spl2_26
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f315,f307,f272,f412]) ).
fof(f412,plain,
( spl2_49
<=> ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_49])]) ).
fof(f315,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X1) )
| ~ spl2_26
| ~ spl2_34 ),
inference(resolution,[],[f308,f273]) ).
fof(f410,plain,
( spl2_48
| ~ spl2_25
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f314,f307,f268,f408]) ).
fof(f408,plain,
( spl2_48
<=> ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_48])]) ).
fof(f314,plain,
( ! [X0,X1] :
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) )
| ~ spl2_25
| ~ spl2_34 ),
inference(resolution,[],[f308,f269]) ).
fof(f406,plain,
( spl2_47
| ~ spl2_24
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f312,f307,f264,f404]) ).
fof(f312,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(implies(X1,X0)) )
| ~ spl2_24
| ~ spl2_34 ),
inference(resolution,[],[f308,f265]) ).
fof(f399,plain,
( ~ spl2_9
| spl2_46 ),
inference(avatar_split_clause,[],[f149,f397,f191]) ).
fof(f191,plain,
( spl2_9
<=> or_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f149,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,[],[f104]) ).
fof(f104,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,[],[f71]) ).
fof(f71,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/sandbox/benchmark/theBenchmark.p',or_3) ).
fof(f394,plain,
( ~ spl2_15
| spl2_45 ),
inference(avatar_split_clause,[],[f148,f392,f221]) ).
fof(f221,plain,
( spl2_15
<=> implies_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f148,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,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/sandbox/benchmark/theBenchmark.p',implies_3) ).
fof(f387,plain,
( ~ spl2_21
| spl2_44 ),
inference(avatar_split_clause,[],[f133,f385,f251]) ).
fof(f251,plain,
( spl2_21
<=> op_equiv ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
fof(f133,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,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/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f382,plain,
( ~ spl2_16
| spl2_43 ),
inference(avatar_split_clause,[],[f144,f380,f226]) ).
fof(f226,plain,
( spl2_16
<=> implies_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f144,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,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/sandbox/benchmark/theBenchmark.p',implies_2) ).
fof(f378,plain,
( spl2_42
| ~ spl2_23
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f311,f307,f260,f376]) ).
fof(f311,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X1,X0)) )
| ~ spl2_23
| ~ spl2_34 ),
inference(resolution,[],[f308,f261]) ).
fof(f367,plain,
( spl2_41
| ~ spl2_28
| ~ spl2_38
| ~ spl2_40 ),
inference(avatar_split_clause,[],[f363,f360,f334,f280,f365]) ).
fof(f360,plain,
( spl2_40
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).
fof(f363,plain,
( ! [X0,X1] : is_a_theorem(or(and(not(X1),X0),implies(X0,X1)))
| ~ spl2_28
| ~ spl2_38
| ~ spl2_40 ),
inference(forward_demodulation,[],[f361,f340]) ).
fof(f361,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ spl2_40 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f362,plain,
( ~ spl2_3
| spl2_40 ),
inference(avatar_split_clause,[],[f143,f360,f161]) ).
fof(f161,plain,
( spl2_3
<=> modus_tollens ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| ~ modus_tollens ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,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/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
fof(f344,plain,
( ~ spl2_19
| spl2_39 ),
inference(avatar_split_clause,[],[f132,f342,f241]) ).
fof(f241,plain,
( spl2_19
<=> op_or ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f132,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,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/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f336,plain,
( spl2_38
| ~ spl2_28
| ~ spl2_37 ),
inference(avatar_split_clause,[],[f332,f329,f280,f334]) ).
fof(f329,plain,
( spl2_37
<=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
fof(f332,plain,
( ! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1)))
| ~ spl2_28
| ~ spl2_37 ),
inference(forward_demodulation,[],[f330,f281]) ).
fof(f330,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ spl2_37 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f331,plain,
( ~ spl2_18
| spl2_37 ),
inference(avatar_split_clause,[],[f131,f329,f236]) ).
fof(f236,plain,
( spl2_18
<=> op_and ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f131,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(f325,plain,
( ~ spl2_20
| spl2_36 ),
inference(avatar_split_clause,[],[f130,f323,f246]) ).
fof(f246,plain,
( spl2_20
<=> op_implies_and ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
fof(f130,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,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/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f321,plain,
( spl2_35
| ~ spl2_22
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f310,f307,f256,f319]) ).
fof(f256,plain,
( spl2_22
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
fof(f310,plain,
( ! [X0,X1] :
( ~ is_a_theorem(X0)
| is_a_theorem(or(X0,X1)) )
| ~ spl2_22
| ~ spl2_34 ),
inference(resolution,[],[f308,f257]) ).
fof(f257,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f309,plain,
( ~ spl2_2
| spl2_34 ),
inference(avatar_split_clause,[],[f147,f307,f156]) ).
fof(f156,plain,
( spl2_2
<=> modus_ponens ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f305,plain,
( ~ spl2_8
| spl2_33 ),
inference(avatar_split_clause,[],[f142,f303,f186]) ).
fof(f186,plain,
( spl2_8
<=> equivalence_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f142,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,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/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
fof(f301,plain,
( ~ spl2_7
| spl2_32 ),
inference(avatar_split_clause,[],[f141,f299,f181]) ).
fof(f181,plain,
( spl2_7
<=> equivalence_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f141,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,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/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
fof(f297,plain,
( ~ spl2_12
| spl2_31 ),
inference(avatar_split_clause,[],[f140,f295,f206]) ).
fof(f206,plain,
( spl2_12
<=> and_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f140,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,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/sandbox/benchmark/theBenchmark.p',and_3) ).
fof(f293,plain,
( ~ spl2_30
| spl2_1 ),
inference(avatar_split_clause,[],[f134,f151,f290]) ).
fof(f151,plain,
( spl2_1
<=> r3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f134,plain,
( r3
| ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( r3
| ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f88,f105]) ).
fof(f105,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0)))
=> ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( r3
| ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
=> r3 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f66,plain,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
fof(f288,plain,
( spl2_29
| ~ spl2_22
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f284,f280,f256,f286]) ).
fof(f284,plain,
( ! [X0,X1] : is_a_theorem(implies(not(X0),implies(X0,X1)))
| ~ spl2_22
| ~ spl2_28 ),
inference(superposition,[],[f257,f281]) ).
fof(f282,plain,
( ~ spl2_17
| spl2_28 ),
inference(avatar_split_clause,[],[f129,f280,f231]) ).
fof(f231,plain,
( spl2_17
<=> op_implies_or ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f129,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f278,plain,
( ~ spl2_5
| spl2_27 ),
inference(avatar_split_clause,[],[f146,f276,f171]) ).
fof(f171,plain,
( spl2_5
<=> substitution_of_equivalents ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f276,plain,
( spl2_27
<=> ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
fof(f146,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,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/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f274,plain,
( ~ spl2_13
| spl2_26 ),
inference(avatar_split_clause,[],[f139,f272,f211]) ).
fof(f211,plain,
( spl2_13
<=> and_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f139,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,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/sandbox/benchmark/theBenchmark.p',and_2) ).
fof(f270,plain,
( ~ spl2_14
| spl2_25 ),
inference(avatar_split_clause,[],[f138,f268,f216]) ).
fof(f216,plain,
( spl2_14
<=> and_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f138,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,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/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f266,plain,
( ~ spl2_4
| spl2_24 ),
inference(avatar_split_clause,[],[f137,f264,f166]) ).
fof(f166,plain,
( spl2_4
<=> implies_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f137,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,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/sandbox/benchmark/theBenchmark.p',implies_1) ).
fof(f262,plain,
( ~ spl2_10
| spl2_23 ),
inference(avatar_split_clause,[],[f136,f260,f196]) ).
fof(f196,plain,
( spl2_10
<=> or_2 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f136,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ or_2 ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,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/sandbox/benchmark/theBenchmark.p',or_2) ).
fof(f258,plain,
( ~ spl2_11
| spl2_22 ),
inference(avatar_split_clause,[],[f135,f256,f201]) ).
fof(f201,plain,
( spl2_11
<=> or_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f135,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,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/sandbox/benchmark/theBenchmark.p',or_1) ).
fof(f254,plain,
spl2_21,
inference(avatar_split_clause,[],[f127,f251]) ).
fof(f127,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f249,plain,
spl2_20,
inference(avatar_split_clause,[],[f126,f246]) ).
fof(f126,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f244,plain,
spl2_19,
inference(avatar_split_clause,[],[f125,f241]) ).
fof(f125,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f239,plain,
spl2_18,
inference(avatar_split_clause,[],[f124,f236]) ).
fof(f124,plain,
op_and,
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f234,plain,
spl2_17,
inference(avatar_split_clause,[],[f123,f231]) ).
fof(f123,plain,
op_implies_or,
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f229,plain,
spl2_16,
inference(avatar_split_clause,[],[f122,f226]) ).
fof(f122,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f224,plain,
spl2_15,
inference(avatar_split_clause,[],[f121,f221]) ).
fof(f121,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f219,plain,
spl2_14,
inference(avatar_split_clause,[],[f120,f216]) ).
fof(f120,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f214,plain,
spl2_13,
inference(avatar_split_clause,[],[f119,f211]) ).
fof(f119,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f209,plain,
spl2_12,
inference(avatar_split_clause,[],[f118,f206]) ).
fof(f118,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f204,plain,
spl2_11,
inference(avatar_split_clause,[],[f117,f201]) ).
fof(f117,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f199,plain,
spl2_10,
inference(avatar_split_clause,[],[f116,f196]) ).
fof(f116,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f194,plain,
spl2_9,
inference(avatar_split_clause,[],[f115,f191]) ).
fof(f115,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
fof(f189,plain,
spl2_8,
inference(avatar_split_clause,[],[f114,f186]) ).
fof(f114,plain,
equivalence_1,
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
fof(f184,plain,
spl2_7,
inference(avatar_split_clause,[],[f113,f181]) ).
fof(f113,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f179,plain,
spl2_6,
inference(avatar_split_clause,[],[f112,f176]) ).
fof(f176,plain,
( spl2_6
<=> equivalence_3 ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f112,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f174,plain,
spl2_5,
inference(avatar_split_clause,[],[f111,f171]) ).
fof(f111,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f169,plain,
spl2_4,
inference(avatar_split_clause,[],[f110,f166]) ).
fof(f110,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f164,plain,
spl2_3,
inference(avatar_split_clause,[],[f109,f161]) ).
fof(f109,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f159,plain,
spl2_2,
inference(avatar_split_clause,[],[f108,f156]) ).
fof(f108,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f154,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f107,f151]) ).
fof(f107,plain,
~ r3,
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
~ r3,
inference(flattening,[],[f54]) ).
fof(f54,negated_conjecture,
~ r3,
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : LCL456+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8042.1875MB
% 0.10/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Apr 29 22:45:56 EDT 2024
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % (18807)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.38 % (18810)WARNING: value z3 for option sas not known
% 0.10/0.38 % (18813)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)
% 0.10/0.38 % (18808)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.38 % (18814)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)
% 0.10/0.38 % (18809)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.38 % (18812)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)
% 0.10/0.38 % (18811)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.38 % (18810)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)
% 0.10/0.38 TRYING [1]
% 0.10/0.38 TRYING [2]
% 0.10/0.38 TRYING [1]
% 0.10/0.38 TRYING [2]
% 0.10/0.39 TRYING [3]
% 0.10/0.39 TRYING [1]
% 0.10/0.39 TRYING [2]
% 0.10/0.39 TRYING [3]
% 0.10/0.40 TRYING [3]
% 0.10/0.40 TRYING [4]
% 0.16/0.41 TRYING [4]
% 0.16/0.42 % (18812)First to succeed.
% 0.16/0.42 % (18812)Refutation found. Thanks to Tanya!
% 0.16/0.42 % SZS status Theorem for theBenchmark
% 0.16/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.43 % (18812)------------------------------
% 0.16/0.43 % (18812)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.43 % (18812)Termination reason: Refutation
% 0.16/0.43
% 0.16/0.43 % (18812)Memory used [KB]: 1934
% 0.16/0.43 % (18812)Time elapsed: 0.046 s
% 0.16/0.43 % (18812)Instructions burned: 81 (million)
% 0.16/0.43 % (18812)------------------------------
% 0.16/0.43 % (18812)------------------------------
% 0.16/0.43 % (18807)Success in time 0.06 s
%------------------------------------------------------------------------------