TSTP Solution File: LCL301-3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL301-3 : TPTP v8.1.2. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 13:41:40 EDT 2024
% Result : Unsatisfiable 0.15s 0.34s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 58
% Syntax : Number of formulae : 180 ( 25 unt; 0 def)
% Number of atoms : 472 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 539 ( 247 ~; 245 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 51 ( 49 usr; 48 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 266 ( 266 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f337,plain,
$false,
inference(avatar_sat_refutation,[],[f23,f27,f31,f37,f41,f47,f51,f55,f60,f65,f71,f76,f80,f85,f90,f96,f106,f116,f120,f131,f135,f139,f150,f154,f158,f166,f174,f178,f182,f186,f215,f219,f228,f232,f237,f248,f252,f259,f268,f272,f279,f285,f289,f293,f297,f332,f336]) ).
fof(f336,plain,
( ~ spl0_24
| spl0_42 ),
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f333,plain,
( $false
| ~ spl0_24
| spl0_42 ),
inference(resolution,[],[f278,f153]) ).
fof(f153,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f152,plain,
( spl0_24
<=> ! [X0] : theorem(or(not(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f278,plain,
( ~ theorem(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))
| spl0_42 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f276,plain,
( spl0_42
<=> theorem(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f332,plain,
( spl0_47
| ~ spl0_5
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f167,f164,f39,f330]) ).
fof(f330,plain,
( spl0_47
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f39,plain,
( spl0_5
<=> ! [X4,X3] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f164,plain,
( spl0_26
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f167,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(X0) )
| ~ spl0_5
| ~ spl0_26 ),
inference(resolution,[],[f165,f40]) ).
fof(f40,plain,
( ! [X3,X4] :
( ~ theorem(or(not(X4),X3))
| theorem(X3)
| ~ theorem(X4) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f165,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f297,plain,
( spl0_46
| ~ spl0_10
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f199,f184,f63,f295]) ).
fof(f295,plain,
( spl0_46
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f63,plain,
( spl0_10
<=> ! [X0] : theorem(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f184,plain,
( spl0_30
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f199,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X0,or(X1,X1))) )
| ~ spl0_10
| ~ spl0_30 ),
inference(resolution,[],[f185,f64]) ).
fof(f64,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f185,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f293,plain,
( spl0_45
| ~ spl0_16
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f170,f164,f94,f291]) ).
fof(f291,plain,
( spl0_45
<=> ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f94,plain,
( spl0_16
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f170,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X0,X1))
| theorem(or(or(X2,X1),X0)) )
| ~ spl0_16
| ~ spl0_26 ),
inference(resolution,[],[f165,f95]) ).
fof(f95,plain,
( ! [X0,X1] :
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f289,plain,
( spl0_44
| ~ spl0_15
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f169,f164,f88,f287]) ).
fof(f287,plain,
( spl0_44
<=> ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f88,plain,
( spl0_15
<=> ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f169,plain,
( ! [X0,X1] :
( ~ theorem(or(or(X0,X1),X1))
| theorem(or(X0,X1)) )
| ~ spl0_15
| ~ spl0_26 ),
inference(resolution,[],[f165,f89]) ).
fof(f89,plain,
( ! [X0] :
( ~ theorem(or(X0,X0))
| theorem(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f285,plain,
( spl0_43
| ~ spl0_5
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f160,f156,f39,f283]) ).
fof(f283,plain,
( spl0_43
<=> ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f156,plain,
( spl0_25
<=> ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f160,plain,
( ! [X0,X1] :
( theorem(or(not(or(X0,not(X1))),X0))
| ~ theorem(X1) )
| ~ spl0_5
| ~ spl0_25 ),
inference(resolution,[],[f157,f40]) ).
fof(f157,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f279,plain,
( ~ spl0_42
| spl0_6
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f273,f266,f44,f276]) ).
fof(f44,plain,
( spl0_6
<=> theorem(not(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f266,plain,
( spl0_40
<=> ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f273,plain,
( ~ theorem(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))
| spl0_6
| ~ spl0_40 ),
inference(resolution,[],[f267,f46]) ).
fof(f46,plain,
( ~ theorem(not(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))))))
| spl0_6 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f267,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f272,plain,
( spl0_41
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f162,f156,f94,f270]) ).
fof(f270,plain,
( spl0_41
<=> ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f162,plain,
( ! [X0,X1] : theorem(or(or(not(or(X0,X1)),X0),X1))
| ~ spl0_16
| ~ spl0_25 ),
inference(resolution,[],[f157,f95]) ).
fof(f268,plain,
( spl0_40
| ~ spl0_5
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f141,f133,f39,f266]) ).
fof(f133,plain,
( spl0_21
<=> ! [X0] : theorem(or(X0,not(or(X0,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f141,plain,
( ! [X0] :
( theorem(not(or(not(X0),not(X0))))
| ~ theorem(X0) )
| ~ spl0_5
| ~ spl0_21 ),
inference(resolution,[],[f134,f40]) ).
fof(f134,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f259,plain,
( spl0_39
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f127,f114,f104,f257]) ).
fof(f257,plain,
( spl0_39
<=> ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f104,plain,
( spl0_17
<=> ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f114,plain,
( spl0_18
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f127,plain,
( ! [X2,X0,X1] :
( ~ theorem(X0)
| theorem(or(X1,or(X0,X2))) )
| ~ spl0_17
| ~ spl0_18 ),
inference(resolution,[],[f115,f105]) ).
fof(f105,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f115,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f252,plain,
( spl0_38
| ~ spl0_16
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f146,f137,f94,f250]) ).
fof(f250,plain,
( spl0_38
<=> ! [X0,X1] : theorem(or(or(not(X0),X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f137,plain,
( spl0_22
<=> ! [X0,X1] : theorem(or(X0,or(not(X1),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f146,plain,
( ! [X0,X1] : theorem(or(or(not(X0),X0),X1))
| ~ spl0_16
| ~ spl0_22 ),
inference(resolution,[],[f138,f95]) ).
fof(f138,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f248,plain,
( spl0_36
| spl0_37
| ~ spl0_5
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f124,f114,f39,f246,f243]) ).
fof(f243,plain,
( spl0_36
<=> ! [X1] : theorem(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f246,plain,
( spl0_37
<=> ! [X0] :
( ~ theorem(not(X0))
| ~ theorem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f124,plain,
( ! [X0,X1] :
( ~ theorem(not(X0))
| theorem(X1)
| ~ theorem(X0) )
| ~ spl0_5
| ~ spl0_18 ),
inference(resolution,[],[f115,f40]) ).
fof(f237,plain,
( spl0_35
| ~ spl0_16
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f189,f152,f94,f235]) ).
fof(f235,plain,
( spl0_35
<=> ! [X0] : theorem(or(X0,not(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f189,plain,
( ! [X0] : theorem(or(X0,not(X0)))
| ~ spl0_16
| ~ spl0_24 ),
inference(resolution,[],[f153,f95]) ).
fof(f232,plain,
( spl0_34
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f111,f104,f83,f230]) ).
fof(f230,plain,
( spl0_34
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f83,plain,
( spl0_14
<=> ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f111,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,X1)),or(not(or(not(X1),X2)),or(X0,X2))))
| ~ spl0_14
| ~ spl0_17 ),
inference(resolution,[],[f105,f84]) ).
fof(f84,plain,
( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f228,plain,
( spl0_33
| ~ spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f101,f94,f83,f226]) ).
fof(f226,plain,
( spl0_33
<=> ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f101,plain,
( ! [X2,X0,X1] : theorem(or(or(not(or(X0,X1)),or(X0,X2)),not(or(not(X1),X2))))
| ~ spl0_14
| ~ spl0_16 ),
inference(resolution,[],[f95,f84]) ).
fof(f219,plain,
( spl0_32
| ~ spl0_16
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f123,f118,f94,f217]) ).
fof(f217,plain,
( spl0_32
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f118,plain,
( spl0_19
<=> ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f123,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(or(X2,X1),not(or(X2,X0)))) )
| ~ spl0_16
| ~ spl0_19 ),
inference(resolution,[],[f119,f95]) ).
fof(f119,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f215,plain,
( spl0_31
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f122,f118,f104,f213]) ).
fof(f213,plain,
( spl0_31
<=> ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f122,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,or(not(or(X2,X0)),X1))) )
| ~ spl0_17
| ~ spl0_19 ),
inference(resolution,[],[f119,f105]) ).
fof(f186,plain,
( spl0_30
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f121,f118,f39,f184]) ).
fof(f121,plain,
( ! [X2,X0,X1] :
( ~ theorem(or(not(X0),X1))
| theorem(or(X2,X1))
| ~ theorem(or(X2,X0)) )
| ~ spl0_5
| ~ spl0_19 ),
inference(resolution,[],[f119,f40]) ).
fof(f182,plain,
( spl0_29
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f110,f104,f63,f180]) ).
fof(f180,plain,
( spl0_29
<=> ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f110,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(or(X0,X1),or(X0,X1))),X1)))
| ~ spl0_10
| ~ spl0_17 ),
inference(resolution,[],[f105,f64]) ).
fof(f178,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f109,f104,f74,f176]) ).
fof(f176,plain,
( spl0_28
<=> ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f74,plain,
( spl0_12
<=> ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f109,plain,
( ! [X2,X0,X1] : theorem(or(X0,or(not(or(X1,or(X0,X2))),or(X1,X2))))
| ~ spl0_12
| ~ spl0_17 ),
inference(resolution,[],[f105,f75]) ).
fof(f75,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f174,plain,
( spl0_27
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f100,f94,f74,f172]) ).
fof(f172,plain,
( spl0_27
<=> ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f100,plain,
( ! [X2,X0,X1] : theorem(or(or(X0,or(X1,X2)),not(or(X1,or(X0,X2)))))
| ~ spl0_12
| ~ spl0_16 ),
inference(resolution,[],[f95,f75]) ).
fof(f166,plain,
( spl0_26
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f112,f104,f78,f164]) ).
fof(f78,plain,
( spl0_13
<=> ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f112,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X0,X2)) )
| ~ spl0_13
| ~ spl0_17 ),
inference(resolution,[],[f105,f79]) ).
fof(f79,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f158,plain,
( spl0_25
| ~ spl0_11
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f108,f104,f69,f156]) ).
fof(f69,plain,
( spl0_11
<=> ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f108,plain,
( ! [X0,X1] : theorem(or(X0,or(not(or(X1,X0)),X1)))
| ~ spl0_11
| ~ spl0_17 ),
inference(resolution,[],[f105,f70]) ).
fof(f70,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f154,plain,
( spl0_24
| ~ spl0_15
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f145,f137,f88,f152]) ).
fof(f145,plain,
( ! [X0] : theorem(or(not(X0),X0))
| ~ spl0_15
| ~ spl0_22 ),
inference(resolution,[],[f138,f89]) ).
fof(f150,plain,
( spl0_23
| ~ spl0_11
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f99,f94,f69,f148]) ).
fof(f148,plain,
( spl0_23
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f99,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(or(X1,X0))))
| ~ spl0_11
| ~ spl0_16 ),
inference(resolution,[],[f95,f70]) ).
fof(f139,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f107,f104,f49,f137]) ).
fof(f49,plain,
( spl0_7
<=> ! [X0,X1] : theorem(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f107,plain,
( ! [X0,X1] : theorem(or(X0,or(not(X1),X1)))
| ~ spl0_7
| ~ spl0_17 ),
inference(resolution,[],[f105,f50]) ).
fof(f50,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f135,plain,
( spl0_21
| ~ spl0_10
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f98,f94,f63,f133]) ).
fof(f98,plain,
( ! [X0] : theorem(or(X0,not(or(X0,X0))))
| ~ spl0_10
| ~ spl0_16 ),
inference(resolution,[],[f95,f64]) ).
fof(f131,plain,
( spl0_20
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f97,f94,f49,f129]) ).
fof(f129,plain,
( spl0_20
<=> ! [X0,X1] : theorem(or(or(X0,X1),not(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f97,plain,
( ! [X0,X1] : theorem(or(or(X0,X1),not(X1)))
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f95,f50]) ).
fof(f120,plain,
( spl0_19
| ~ spl0_5
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f86,f83,f39,f118]) ).
fof(f86,plain,
( ! [X2,X0,X1] :
( theorem(or(not(or(X0,X1)),or(X0,X2)))
| ~ theorem(or(not(X1),X2)) )
| ~ spl0_5
| ~ spl0_14 ),
inference(resolution,[],[f84,f40]) ).
fof(f116,plain,
( spl0_18
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f102,f94,f78,f114]) ).
fof(f102,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X0) )
| ~ spl0_13
| ~ spl0_16 ),
inference(resolution,[],[f95,f79]) ).
fof(f106,plain,
( spl0_17
| ~ spl0_5
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f81,f74,f39,f104]) ).
fof(f81,plain,
( ! [X2,X0,X1] :
( theorem(or(X0,or(X1,X2)))
| ~ theorem(or(X1,or(X0,X2))) )
| ~ spl0_5
| ~ spl0_12 ),
inference(resolution,[],[f75,f40]) ).
fof(f96,plain,
( spl0_16
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f72,f69,f39,f94]) ).
fof(f72,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(or(X1,X0)) )
| ~ spl0_5
| ~ spl0_11 ),
inference(resolution,[],[f70,f40]) ).
fof(f90,plain,
( spl0_15
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f67,f63,f39,f88]) ).
fof(f67,plain,
( ! [X0] :
( theorem(X0)
| ~ theorem(or(X0,X0)) )
| ~ spl0_5
| ~ spl0_10 ),
inference(resolution,[],[f64,f40]) ).
fof(f85,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f61,f58,f21,f83]) ).
fof(f21,plain,
( spl0_1
<=> ! [X3] :
( ~ axiom(X3)
| theorem(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f58,plain,
( spl0_9
<=> ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f61,plain,
( ! [X2,X0,X1] : theorem(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_1
| ~ spl0_9 ),
inference(resolution,[],[f59,f22]) ).
fof(f22,plain,
( ! [X3] :
( ~ axiom(X3)
| theorem(X3) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f21]) ).
fof(f59,plain,
( ! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1))))
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f58]) ).
fof(f80,plain,
( spl0_13
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f66,f49,f39,f78]) ).
fof(f66,plain,
( ! [X0,X1] :
( theorem(or(X0,X1))
| ~ theorem(X1) )
| ~ spl0_5
| ~ spl0_7 ),
inference(resolution,[],[f50,f40]) ).
fof(f76,plain,
( spl0_12
| ~ spl0_1
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f56,f53,f21,f74]) ).
fof(f53,plain,
( spl0_8
<=> ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f56,plain,
( ! [X2,X0,X1] : theorem(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f54,f22]) ).
fof(f54,plain,
( ! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2))))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f71,plain,
( spl0_11
| ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f42,f35,f21,f69]) ).
fof(f35,plain,
( spl0_4
<=> ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f42,plain,
( ! [X0,X1] : theorem(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_1
| ~ spl0_4 ),
inference(resolution,[],[f36,f22]) ).
fof(f36,plain,
( ! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0)))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f65,plain,
( spl0_10
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f33,f29,f21,f63]) ).
fof(f29,plain,
( spl0_3
<=> ! [X0] : axiom(or(not(or(X0,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f33,plain,
( ! [X0] : theorem(or(not(or(X0,X0)),X0))
| ~ spl0_1
| ~ spl0_3 ),
inference(resolution,[],[f30,f22]) ).
fof(f30,plain,
( ! [X0] : axiom(or(not(or(X0,X0)),X0))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f60,plain,
spl0_9,
inference(avatar_split_clause,[],[f17,f58]) ).
fof(f17,plain,
! [X2,X0,X1] : axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(definition_unfolding,[],[f5,f6,f6,f6]) ).
fof(f6,axiom,
! [X3,X4] : implies(X3,X4) = or(not(X3),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
fof(f5,axiom,
! [X2,X0,X1] : axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f55,plain,
spl0_8,
inference(avatar_split_clause,[],[f18,f53]) ).
fof(f18,plain,
! [X2,X0,X1] : axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(definition_unfolding,[],[f4,f6]) ).
fof(f4,axiom,
! [X2,X0,X1] : axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f51,plain,
( spl0_7
| ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f32,f25,f21,f49]) ).
fof(f25,plain,
( spl0_2
<=> ! [X0,X1] : axiom(or(not(X0),or(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f32,plain,
( ! [X0,X1] : theorem(or(not(X0),or(X1,X0)))
| ~ spl0_1
| ~ spl0_2 ),
inference(resolution,[],[f26,f22]) ).
fof(f26,plain,
( ! [X0,X1] : axiom(or(not(X0),or(X1,X0)))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f47,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f13,f44]) ).
fof(f13,plain,
~ theorem(not(or(not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q))))),not(or(not(not(or(not(not(p)),not(q)))),not(or(not(not(p)),not(q)))))))),
inference(definition_unfolding,[],[f11,f12,f6,f9]) ).
fof(f9,axiom,
! [X6,X5] : and(X5,X6) = not(or(not(X5),not(X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_defn) ).
fof(f12,plain,
! [X6,X5] : equivalent(X5,X6) = not(or(not(or(not(X5),X6)),not(or(not(X6),X5)))),
inference(definition_unfolding,[],[f10,f9,f6,f6]) ).
fof(f10,axiom,
! [X6,X5] : equivalent(X5,X6) = and(implies(X5,X6),implies(X6,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalent_defn) ).
fof(f11,axiom,
~ theorem(equivalent(not(implies(not(p),not(q))),and(not(p),q))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f41,plain,
spl0_5,
inference(avatar_split_clause,[],[f19,f39]) ).
fof(f19,plain,
! [X3,X4] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(or(not(X4),X3)) ),
inference(definition_unfolding,[],[f8,f6]) ).
fof(f8,axiom,
! [X3,X4] :
( ~ theorem(X4)
| theorem(X3)
| ~ theorem(implies(X4,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f37,plain,
spl0_4,
inference(avatar_split_clause,[],[f16,f35]) ).
fof(f16,plain,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(definition_unfolding,[],[f3,f6]) ).
fof(f3,axiom,
! [X0,X1] : axiom(implies(or(X0,X1),or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f31,plain,
spl0_3,
inference(avatar_split_clause,[],[f15,f29]) ).
fof(f15,plain,
! [X0] : axiom(or(not(or(X0,X0)),X0)),
inference(definition_unfolding,[],[f1,f6]) ).
fof(f1,axiom,
! [X0] : axiom(implies(or(X0,X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f27,plain,
spl0_2,
inference(avatar_split_clause,[],[f14,f25]) ).
fof(f14,plain,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))),
inference(definition_unfolding,[],[f2,f6]) ).
fof(f2,axiom,
! [X0,X1] : axiom(implies(X0,or(X1,X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f23,plain,
spl0_1,
inference(avatar_split_clause,[],[f7,f21]) ).
fof(f7,axiom,
! [X3] :
( ~ axiom(X3)
| theorem(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL301-3 : TPTP v8.1.2. Released v2.3.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.31 % Computer : n024.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Mon Apr 29 23:02:51 EDT 2024
% 0.09/0.32 % CPUTime :
% 0.09/0.32 % (1472)Running in auto input_syntax mode. Trying TPTP
% 0.09/0.33 % (1475)WARNING: value z3 for option sas not known
% 0.09/0.33 % (1479)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)
% 0.09/0.33 % (1474)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.09/0.33 % (1477)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)
% 0.09/0.33 % (1475)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)
% 0.09/0.33 % (1473)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.09/0.33 % (1476)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.09/0.34 TRYING [1]
% 0.09/0.34 % (1478)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)
% 0.09/0.34 TRYING [1]
% 0.09/0.34 TRYING [2]
% 0.09/0.34 TRYING [2]
% 0.09/0.34 TRYING [3]
% 0.09/0.34 TRYING [3]
% 0.09/0.34 % (1477)First to succeed.
% 0.15/0.34 % (1477)Refutation found. Thanks to Tanya!
% 0.15/0.34 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.35 % (1477)------------------------------
% 0.15/0.35 % (1477)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.35 % (1477)Termination reason: Refutation
% 0.15/0.35
% 0.15/0.35 % (1477)Memory used [KB]: 975
% 0.15/0.35 % (1477)Time elapsed: 0.010 s
% 0.15/0.35 % (1477)Instructions burned: 15 (million)
% 0.15/0.35 % (1477)------------------------------
% 0.15/0.35 % (1477)------------------------------
% 0.15/0.35 % (1472)Success in time 0.024 s
%------------------------------------------------------------------------------