%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG036+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:20:34 AM UTC 2026
% Result : Theorem 0.35s 0.43s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 156 ( 14 unt; 18 def)
% Number of atoms : 573 ( 252 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 570 ( 153 ~; 327 |; 72 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
( op(unit,e0) = e0
& op(e0,unit) = e0
& op(unit,e1) = e1
& op(e1,unit) = e1
& op(unit,e2) = e2
& op(e2,unit) = e2
& op(unit,e3) = e3
& op(e3,unit) = e3
& ( unit = e0
| unit = e1
| unit = e2
| unit = e3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f4,axiom,
unit = e0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f7,conjecture,
( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f8,negated_conjecture,
~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( ( e0 != op(e0,e0)
| e0 != op(e1,e1)
| e0 != op(e2,e2)
| e0 != op(e3,e3) )
& ( op(e0,e0) != e1
| e1 != op(e1,e1)
| e1 != op(e2,e2)
| e1 != op(e3,e3) )
& ( op(e0,e0) != e2
| e2 != op(e1,e1)
| e2 != op(e2,e2)
| e2 != op(e3,e3) )
& ( op(e0,e0) != e3
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| e3 != op(e3,e3) )
& ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f33,plain,
e0 = op(e0,unit),
inference(cnf_transformation,[],[f2]) ).
fof(f67,plain,
e0 = unit,
inference(cnf_transformation,[],[f4]) ).
fof(f122,plain,
( e0 = op(e3,e3)
| ~ sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f123,plain,
( e0 = op(e2,e2)
| ~ sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f124,plain,
( e0 = op(e1,e1)
| ~ sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f126,plain,
( e1 = op(e3,e3)
| ~ sP0 ),
inference(cnf_transformation,[],[f9]) ).
fof(f127,plain,
( e1 = op(e2,e2)
| ~ sP0 ),
inference(cnf_transformation,[],[f9]) ).
fof(f128,plain,
( e1 = op(e1,e1)
| ~ sP0 ),
inference(cnf_transformation,[],[f9]) ).
fof(f129,plain,
( op(e0,e0) = e1
| ~ sP0 ),
inference(cnf_transformation,[],[f9]) ).
fof(f130,plain,
( op(e0,e0) = e3
| e2 = op(e3,e3)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f131,plain,
( op(e0,e0) = e3
| e2 = op(e2,e2)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f132,plain,
( op(e0,e0) = e3
| e2 = op(e1,e1)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f133,plain,
( op(e0,e0) = e3
| op(e0,e0) = e2
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f134,plain,
( e3 = op(e1,e1)
| e2 = op(e3,e3)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f135,plain,
( e3 = op(e1,e1)
| e2 = op(e2,e2)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f136,plain,
( e3 = op(e1,e1)
| e2 = op(e1,e1)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f137,plain,
( e3 = op(e1,e1)
| op(e0,e0) = e2
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f138,plain,
( e3 = op(e2,e2)
| e2 = op(e3,e3)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f139,plain,
( e3 = op(e2,e2)
| e2 = op(e2,e2)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f140,plain,
( e3 = op(e2,e2)
| e2 = op(e1,e1)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f141,plain,
( e3 = op(e2,e2)
| op(e0,e0) = e2
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f142,plain,
( e3 = op(e3,e3)
| e2 = op(e3,e3)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f143,plain,
( e3 = op(e3,e3)
| e2 = op(e2,e2)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f144,plain,
( e3 = op(e3,e3)
| e2 = op(e1,e1)
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f145,plain,
( e3 = op(e3,e3)
| op(e0,e0) = e2
| sP0
| sP1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f146,plain,
( e0 != op(e3,e3)
| e0 != op(e2,e2)
| e0 != op(e1,e1)
| e0 != op(e0,e0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f147,plain,
( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| op(e0,e0) != e1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f148,plain,
( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| op(e0,e0) != e2 ),
inference(cnf_transformation,[],[f9]) ).
fof(f149,plain,
( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| op(e0,e0) != e3 ),
inference(cnf_transformation,[],[f9]) ).
fof(f167,plain,
unit = op(unit,unit),
inference(definition_unfolding,[],[f33,f67,f67]) ).
fof(f234,plain,
( e3 != op(e3,e3)
| e3 != op(e2,e2)
| e3 != op(e1,e1)
| e3 != op(unit,unit) ),
inference(definition_unfolding,[],[f149,f67,f67]) ).
fof(f235,plain,
( e2 != op(e3,e3)
| e2 != op(e2,e2)
| e2 != op(e1,e1)
| e2 != op(unit,unit) ),
inference(definition_unfolding,[],[f148,f67,f67]) ).
fof(f236,plain,
( e1 != op(e3,e3)
| e1 != op(e2,e2)
| e1 != op(e1,e1)
| e1 != op(unit,unit) ),
inference(definition_unfolding,[],[f147,f67,f67]) ).
fof(f237,plain,
( op(e3,e3) != unit
| op(e2,e2) != unit
| op(e1,e1) != unit
| unit != op(unit,unit) ),
inference(definition_unfolding,[],[f146,f67,f67,f67,f67,f67,f67]) ).
fof(f238,plain,
( e3 = op(e3,e3)
| e2 = op(unit,unit)
| sP0
| sP1 ),
inference(definition_unfolding,[],[f145,f67,f67]) ).
fof(f239,plain,
( e3 = op(e2,e2)
| e2 = op(unit,unit)
| sP0
| sP1 ),
inference(definition_unfolding,[],[f141,f67,f67]) ).
fof(f240,plain,
( e3 = op(e1,e1)
| e2 = op(unit,unit)
| sP0
| sP1 ),
inference(definition_unfolding,[],[f137,f67,f67]) ).
fof(f241,plain,
( e3 = op(unit,unit)
| e2 = op(unit,unit)
| sP0
| sP1 ),
inference(definition_unfolding,[],[f133,f67,f67,f67,f67]) ).
fof(f242,plain,
( e3 = op(unit,unit)
| e2 = op(e1,e1)
| sP0
| sP1 ),
inference(definition_unfolding,[],[f132,f67,f67]) ).
fof(f243,plain,
( e3 = op(unit,unit)
| e2 = op(e2,e2)
| sP0
| sP1 ),
inference(definition_unfolding,[],[f131,f67,f67]) ).
fof(f244,plain,
( e3 = op(unit,unit)
| e2 = op(e3,e3)
| sP0
| sP1 ),
inference(definition_unfolding,[],[f130,f67,f67]) ).
fof(f245,plain,
( e1 = op(unit,unit)
| ~ sP0 ),
inference(definition_unfolding,[],[f129,f67,f67]) ).
fof(f247,plain,
( op(e1,e1) = unit
| ~ sP1 ),
inference(definition_unfolding,[],[f124,f67]) ).
fof(f248,plain,
( op(e2,e2) = unit
| ~ sP1 ),
inference(definition_unfolding,[],[f123,f67]) ).
fof(f249,plain,
( op(e3,e3) = unit
| ~ sP1 ),
inference(definition_unfolding,[],[f122,f67]) ).
fof(f250,plain,
( e3 = op(e3,e3)
| e2 = op(unit,unit)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f238]) ).
fof(f251,plain,
( e3 = op(e3,e3)
| e2 = op(e1,e1)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f144]) ).
fof(f252,plain,
( e3 = op(e3,e3)
| e2 = op(e2,e2)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f143]) ).
fof(f253,plain,
( e3 = op(e3,e3)
| e2 = op(e3,e3)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f142]) ).
fof(f254,plain,
( e3 = op(e2,e2)
| e2 = op(unit,unit)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f239]) ).
fof(f255,plain,
( e3 = op(e2,e2)
| e2 = op(e1,e1)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f140]) ).
fof(f256,plain,
( e3 = op(e2,e2)
| e2 = op(e2,e2)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f139]) ).
fof(f257,plain,
( e3 = op(e2,e2)
| e2 = op(e3,e3)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f138]) ).
fof(f258,plain,
( e3 = op(e1,e1)
| e2 = op(unit,unit)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f240]) ).
fof(f259,plain,
( e3 = op(e1,e1)
| e2 = op(e1,e1)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f136]) ).
fof(f260,plain,
( e3 = op(e1,e1)
| e2 = op(e2,e2)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f135]) ).
fof(f261,plain,
( e3 = op(e1,e1)
| e2 = op(e3,e3)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f134]) ).
fof(f262,plain,
( e3 = op(unit,unit)
| e2 = op(unit,unit)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f241]) ).
fof(f263,plain,
( e3 = op(unit,unit)
| e2 = op(e1,e1)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f242]) ).
fof(f264,plain,
( e3 = op(unit,unit)
| e2 = op(e2,e2)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f243]) ).
fof(f265,plain,
( e3 = op(unit,unit)
| e2 = op(e3,e3)
| sP0
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f244]) ).
fof(f267,plain,
( op(e1,e1) = unit
| sP1 ),
inference(consistent_polarity_flipping,[],[f247]) ).
fof(f268,plain,
( op(e2,e2) = unit
| sP1 ),
inference(consistent_polarity_flipping,[],[f248]) ).
fof(f269,plain,
( op(e3,e3) = unit
| sP1 ),
inference(consistent_polarity_flipping,[],[f249]) ).
fof(f271,definition,
( spl2_1
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f275,definition,
( spl2_2
<=> op(e3,e3) = unit ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f278,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f269,f275,f271]) ).
fof(f280,definition,
( spl2_3
<=> op(e2,e2) = unit ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f283,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f268,f280,f271]) ).
fof(f285,definition,
( spl2_4
<=> op(e1,e1) = unit ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f288,plain,
( spl2_1
| spl2_4 ),
inference(avatar_split_clause,[],[f267,f285,f271]) ).
fof(f290,definition,
( spl2_5
<=> unit = op(unit,unit) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f295,definition,
( spl2_6
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f299,definition,
( spl2_7
<=> e1 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f302,plain,
( ~ spl2_6
| spl2_7 ),
inference(avatar_split_clause,[],[f126,f299,f295]) ).
fof(f304,definition,
( spl2_8
<=> e1 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f307,plain,
( ~ spl2_6
| spl2_8 ),
inference(avatar_split_clause,[],[f127,f304,f295]) ).
fof(f309,definition,
( spl2_9
<=> e1 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f312,plain,
( ~ spl2_6
| spl2_9 ),
inference(avatar_split_clause,[],[f128,f309,f295]) ).
fof(f314,definition,
( spl2_10
<=> e1 = op(unit,unit) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f317,plain,
( ~ spl2_6
| spl2_10 ),
inference(avatar_split_clause,[],[f245,f314,f295]) ).
fof(f319,definition,
( spl2_11
<=> e2 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f323,definition,
( spl2_12
<=> e3 = op(unit,unit) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f326,plain,
( ~ spl2_1
| spl2_6
| spl2_11
| spl2_12 ),
inference(avatar_split_clause,[],[f265,f323,f319,f295,f271]) ).
fof(f328,definition,
( spl2_13
<=> e2 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f331,plain,
( ~ spl2_1
| spl2_6
| spl2_13
| spl2_12 ),
inference(avatar_split_clause,[],[f264,f323,f328,f295,f271]) ).
fof(f333,definition,
( spl2_14
<=> e2 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl2_14])],[avatar_definition]) ).
fof(f336,plain,
( ~ spl2_1
| spl2_6
| spl2_14
| spl2_12 ),
inference(avatar_split_clause,[],[f263,f323,f333,f295,f271]) ).
fof(f338,definition,
( spl2_15
<=> e2 = op(unit,unit) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f341,plain,
( ~ spl2_1
| spl2_6
| spl2_15
| spl2_12 ),
inference(avatar_split_clause,[],[f262,f323,f338,f295,f271]) ).
fof(f343,definition,
( spl2_16
<=> e3 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f346,plain,
( ~ spl2_1
| spl2_6
| spl2_11
| spl2_16 ),
inference(avatar_split_clause,[],[f261,f343,f319,f295,f271]) ).
fof(f347,plain,
( ~ spl2_1
| spl2_6
| spl2_13
| spl2_16 ),
inference(avatar_split_clause,[],[f260,f343,f328,f295,f271]) ).
fof(f348,plain,
( ~ spl2_1
| spl2_6
| spl2_14
| spl2_16 ),
inference(avatar_split_clause,[],[f259,f343,f333,f295,f271]) ).
fof(f349,plain,
( ~ spl2_1
| spl2_6
| spl2_15
| spl2_16 ),
inference(avatar_split_clause,[],[f258,f343,f338,f295,f271]) ).
fof(f351,definition,
( spl2_17
<=> e3 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl2_17])],[avatar_definition]) ).
fof(f354,plain,
( ~ spl2_1
| spl2_6
| spl2_11
| spl2_17 ),
inference(avatar_split_clause,[],[f257,f351,f319,f295,f271]) ).
fof(f355,plain,
( ~ spl2_1
| spl2_6
| spl2_13
| spl2_17 ),
inference(avatar_split_clause,[],[f256,f351,f328,f295,f271]) ).
fof(f356,plain,
( ~ spl2_1
| spl2_6
| spl2_14
| spl2_17 ),
inference(avatar_split_clause,[],[f255,f351,f333,f295,f271]) ).
fof(f357,plain,
( ~ spl2_1
| spl2_6
| spl2_15
| spl2_17 ),
inference(avatar_split_clause,[],[f254,f351,f338,f295,f271]) ).
fof(f359,definition,
( spl2_18
<=> e3 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl2_18])],[avatar_definition]) ).
fof(f362,plain,
( ~ spl2_1
| spl2_6
| spl2_11
| spl2_18 ),
inference(avatar_split_clause,[],[f253,f359,f319,f295,f271]) ).
fof(f363,plain,
( ~ spl2_1
| spl2_6
| spl2_13
| spl2_18 ),
inference(avatar_split_clause,[],[f252,f359,f328,f295,f271]) ).
fof(f364,plain,
( ~ spl2_1
| spl2_6
| spl2_14
| spl2_18 ),
inference(avatar_split_clause,[],[f251,f359,f333,f295,f271]) ).
fof(f365,plain,
( ~ spl2_1
| spl2_6
| spl2_15
| spl2_18 ),
inference(avatar_split_clause,[],[f250,f359,f338,f295,f271]) ).
fof(f366,plain,
( ~ spl2_5
| ~ spl2_4
| ~ spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f237,f275,f280,f285,f290]) ).
fof(f367,plain,
( ~ spl2_10
| ~ spl2_9
| ~ spl2_8
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f236,f299,f304,f309,f314]) ).
fof(f368,plain,
( ~ spl2_15
| ~ spl2_14
| ~ spl2_13
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f235,f319,f328,f333,f338]) ).
fof(f369,plain,
( ~ spl2_12
| ~ spl2_16
| ~ spl2_17
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f234,f359,f351,f343,f323]) ).
fof(f600,plain,
spl2_5,
inference(avatar_split_clause,[],[f167,f290]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f278]) ).
cnf(s2,plain,
( spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f283]) ).
cnf(s3,plain,
( spl2_1
| spl2_4 ),
inference(sat_conversion,[],[f288]) ).
cnf(s5,plain,
( ~ spl2_6
| spl2_7 ),
inference(sat_conversion,[],[f302]) ).
cnf(s6,plain,
( ~ spl2_6
| spl2_8 ),
inference(sat_conversion,[],[f307]) ).
cnf(s7,plain,
( ~ spl2_6
| spl2_9 ),
inference(sat_conversion,[],[f312]) ).
cnf(s8,plain,
( ~ spl2_6
| spl2_10 ),
inference(sat_conversion,[],[f317]) ).
cnf(s9,plain,
( ~ spl2_1
| spl2_6
| spl2_11
| spl2_12 ),
inference(sat_conversion,[],[f326]) ).
cnf(s10,plain,
( ~ spl2_1
| spl2_6
| spl2_12
| spl2_13 ),
inference(sat_conversion,[],[f331]) ).
cnf(s11,plain,
( ~ spl2_1
| spl2_6
| spl2_12
| spl2_14 ),
inference(sat_conversion,[],[f336]) ).
cnf(s12,plain,
( ~ spl2_1
| spl2_6
| spl2_12
| spl2_15 ),
inference(sat_conversion,[],[f341]) ).
cnf(s13,plain,
( ~ spl2_1
| spl2_6
| spl2_11
| spl2_16 ),
inference(sat_conversion,[],[f346]) ).
cnf(s14,plain,
( ~ spl2_1
| spl2_6
| spl2_13
| spl2_16 ),
inference(sat_conversion,[],[f347]) ).
cnf(s15,plain,
( ~ spl2_1
| spl2_6
| spl2_14
| spl2_16 ),
inference(sat_conversion,[],[f348]) ).
cnf(s16,plain,
( ~ spl2_1
| spl2_6
| spl2_15
| spl2_16 ),
inference(sat_conversion,[],[f349]) ).
cnf(s17,plain,
( ~ spl2_1
| spl2_6
| spl2_11
| spl2_17 ),
inference(sat_conversion,[],[f354]) ).
cnf(s18,plain,
( ~ spl2_1
| spl2_6
| spl2_13
| spl2_17 ),
inference(sat_conversion,[],[f355]) ).
cnf(s19,plain,
( ~ spl2_1
| spl2_6
| spl2_14
| spl2_17 ),
inference(sat_conversion,[],[f356]) ).
cnf(s20,plain,
( ~ spl2_1
| spl2_6
| spl2_15
| spl2_17 ),
inference(sat_conversion,[],[f357]) ).
cnf(s21,plain,
( ~ spl2_1
| spl2_6
| spl2_11
| spl2_18 ),
inference(sat_conversion,[],[f362]) ).
cnf(s22,plain,
( ~ spl2_1
| spl2_6
| spl2_13
| spl2_18 ),
inference(sat_conversion,[],[f363]) ).
cnf(s23,plain,
( ~ spl2_1
| spl2_6
| spl2_14
| spl2_18 ),
inference(sat_conversion,[],[f364]) ).
cnf(s24,plain,
( ~ spl2_1
| spl2_6
| spl2_15
| spl2_18 ),
inference(sat_conversion,[],[f365]) ).
cnf(s25,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f366]) ).
cnf(s26,plain,
( ~ spl2_7
| ~ spl2_8
| ~ spl2_9
| ~ spl2_10 ),
inference(sat_conversion,[],[f367]) ).
cnf(s27,plain,
( ~ spl2_11
| ~ spl2_13
| ~ spl2_14
| ~ spl2_15 ),
inference(sat_conversion,[],[f368]) ).
cnf(s28,plain,
( ~ spl2_12
| ~ spl2_16
| ~ spl2_17
| ~ spl2_18 ),
inference(sat_conversion,[],[f369]) ).
cnf(s67,plain,
spl2_5,
inference(sat_conversion,[],[f600]) ).
cnf(s85,plain,
( ~ spl2_2
| ~ spl2_3
| ~ spl2_4 ),
inference(rat,[],[s25,s67]) ).
cnf(s86,plain,
spl2_1,
inference(rat,[],[s85,s1,s2,s3]) ).
cnf(s87,plain,
( spl2_11
| spl2_6 ),
inference(rat,[],[s28,s13,s17,s21,s9,s86]) ).
cnf(s88,plain,
( spl2_18
| spl2_6 ),
inference(rat,[],[s27,s22,s23,s24,s87,s86]) ).
cnf(s89,plain,
( spl2_17
| spl2_6 ),
inference(rat,[],[s27,s18,s19,s20,s87,s86]) ).
cnf(s90,plain,
( spl2_16
| spl2_6 ),
inference(rat,[],[s27,s14,s15,s16,s87,s86]) ).
cnf(s91,plain,
spl2_6,
inference(rat,[],[s27,s10,s11,s12,s28,s90,s89,s88,s87,s86]) ).
cnf(s92,plain,
spl2_10,
inference(rat,[],[s8,s91]) ).
cnf(s93,plain,
spl2_9,
inference(rat,[],[s7,s91]) ).
cnf(s94,plain,
spl2_8,
inference(rat,[],[s6,s91]) ).
cnf(s95,plain,
spl2_7,
inference(rat,[],[s5,s91]) ).
cnf(s96,plain,
$false,
inference(rat,[],[s26,s95,s93,s92,s94]) ).
fof(f617,plain,
$false,
inference(avatar_sat_refutation,[],[s96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG036+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.29/0.31 % Computer : n017.cluster.edu
% 0.29/0.31 % Model : x86_64 x86_64
% 0.29/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.31 % Memory : 8046.5625MB
% 0.29/0.31 % OS : Linux 6.8.0-71-generic
% 0.29/0.31 % CPULimit : 300
% 0.29/0.31 % WCLimit : 300
% 0.29/0.31 % DateTime : Mon Sep 28 19:15:06 UTC 2026
% 0.29/0.32 % CPUTime :
% 0.29/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.29/0.36 Running first-order model finding
% 0.29/0.36 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.43 % (3917150)Will run a generic schedule for satisfiability detection.
% 0.35/0.43 % (3917156)% WARNING: option uhcvi not known.
% 0.35/0.43 % (3917156)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3513757073:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.35/0.43 % (3917156) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3917150-3917156"...
% 0.35/0.43 % (3917156)...printing done.
% 0.35/0.43 % (3917156)Refutation found. Thanks to Tanya!
% 0.35/0.43 % SZS status Theorem for theBenchmark
% 0.35/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.43 % (3917156)------------------------------
% 0.35/0.43 % (3917156)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.43 % (3917156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.43 % (3917156)CaDiCaL version: 2.1.3
% 0.35/0.43 % (3917156)Termination reason: Refutation
% 0.35/0.43 % (3917156)Time elapsed: 0.007 s
% 0.35/0.43 % (3917156)Peak memory usage: 12 MB
% 0.35/0.43 % (3917156)Instructions burned: 12 (million)
% 0.35/0.43 % (3917150)Success in time 0.05 s
% 0.35/0.43 % Vampire exiting
%------------------------------------------------------------------------------