%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG039+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 09:20:35 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 109 ( 21 unt; 20 def)
% Number of atoms : 541 ( 366 equ)
% Maximal formula atoms : 64 ( 4 avg)
% Number of connectives : 618 ( 186 ~; 220 |; 195 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( ( op(e0,e0) = e0
| op(e0,e0) = e1
| op(e0,e0) = e2
| op(e0,e0) = e3 )
& ( op(e0,e1) = e0
| op(e0,e1) = e1
| op(e0,e1) = e2
| op(e0,e1) = e3 )
& ( op(e0,e2) = e0
| op(e0,e2) = e1
| op(e0,e2) = e2
| op(e0,e2) = e3 )
& ( op(e0,e3) = e0
| op(e0,e3) = e1
| op(e0,e3) = e2
| op(e0,e3) = e3 )
& ( op(e1,e0) = e0
| op(e1,e0) = e1
| op(e1,e0) = e2
| op(e1,e0) = e3 )
& ( op(e1,e1) = e0
| op(e1,e1) = e1
| op(e1,e1) = e2
| op(e1,e1) = e3 )
& ( op(e1,e2) = e0
| op(e1,e2) = e1
| op(e1,e2) = e2
| op(e1,e2) = e3 )
& ( op(e1,e3) = e0
| op(e1,e3) = e1
| op(e1,e3) = e2
| op(e1,e3) = e3 )
& ( op(e2,e0) = e0
| op(e2,e0) = e1
| op(e2,e0) = e2
| op(e2,e0) = e3 )
& ( op(e2,e1) = e0
| op(e2,e1) = e1
| op(e2,e1) = e2
| op(e2,e1) = e3 )
& ( op(e2,e2) = e0
| op(e2,e2) = e1
| op(e2,e2) = e2
| op(e2,e2) = e3 )
& ( op(e2,e3) = e0
| op(e2,e3) = e1
| op(e2,e3) = e2
| op(e2,e3) = e3 )
& ( op(e3,e0) = e0
| op(e3,e0) = e1
| op(e3,e0) = e2
| op(e3,e0) = e3 )
& ( op(e3,e1) = e0
| op(e3,e1) = e1
| op(e3,e1) = e2
| op(e3,e1) = e3 )
& ( op(e3,e2) = e0
| op(e3,e2) = e1
| op(e3,e2) = e2
| op(e3,e2) = e3 )
& ( op(e3,e3) = e0
| op(e3,e3) = e1
| op(e3,e3) = e2
| op(e3,e3) = e3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f4,axiom,
( op(e0,e0) != op(e1,e0)
& op(e0,e0) != op(e2,e0)
& op(e0,e0) != op(e3,e0)
& op(e1,e0) != op(e2,e0)
& op(e1,e0) != op(e3,e0)
& op(e2,e0) != op(e3,e0)
& op(e0,e1) != op(e1,e1)
& op(e0,e1) != op(e2,e1)
& op(e0,e1) != op(e3,e1)
& op(e1,e1) != op(e2,e1)
& op(e1,e1) != op(e3,e1)
& op(e2,e1) != op(e3,e1)
& op(e0,e2) != op(e1,e2)
& op(e0,e2) != op(e2,e2)
& op(e0,e2) != op(e3,e2)
& op(e1,e2) != op(e2,e2)
& op(e1,e2) != op(e3,e2)
& op(e2,e2) != op(e3,e2)
& op(e0,e3) != op(e1,e3)
& op(e0,e3) != op(e2,e3)
& op(e0,e3) != op(e3,e3)
& op(e1,e3) != op(e2,e3)
& op(e1,e3) != op(e3,e3)
& op(e2,e3) != op(e3,e3)
& op(e0,e0) != op(e0,e1)
& op(e0,e0) != op(e0,e2)
& op(e0,e0) != op(e0,e3)
& op(e0,e1) != op(e0,e2)
& op(e0,e1) != op(e0,e3)
& op(e0,e2) != op(e0,e3)
& op(e1,e0) != op(e1,e1)
& op(e1,e0) != op(e1,e2)
& op(e1,e0) != op(e1,e3)
& op(e1,e1) != op(e1,e2)
& op(e1,e1) != op(e1,e3)
& op(e1,e2) != op(e1,e3)
& op(e2,e0) != op(e2,e1)
& op(e2,e0) != op(e2,e2)
& op(e2,e0) != op(e2,e3)
& op(e2,e1) != op(e2,e2)
& op(e2,e1) != op(e2,e3)
& op(e2,e2) != op(e2,e3)
& op(e3,e0) != op(e3,e1)
& op(e3,e0) != op(e3,e2)
& op(e3,e0) != op(e3,e3)
& op(e3,e1) != op(e3,e2)
& op(e3,e1) != op(e3,e3)
& op(e3,e2) != op(e3,e3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f6,axiom,
( e0 = op(e1,e1)
& e2 = op(e3,e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
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/sandbox2/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,
( ( ( 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(flattening,[],[f8]) ).
fof(f10,plain,
( ( ( 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 ) )
& ( 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) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f11,plain,
( ( ( 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 ) )
& ( 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) ) ),
inference(flattening,[],[f10]) ).
fof(f12,definition,
( ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f13,definition,
( ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f14,definition,
( ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f15,plain,
( ( ( op(e0,e0) = e0
& op(e1,e1) = e0
& op(e2,e2) = e0
& op(e3,e3) = e0 )
| sP2
| sP1
| sP0 )
& ( 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) ) ),
inference(definition_folding,[],[f11,f14,f13,f12]) ).
fof(f16,plain,
( ( op(e0,e0) = e1
& op(e1,e1) = e1
& op(e2,e2) = e1
& op(e3,e3) = e1 )
| ~ sP2 ),
inference(nnf_transformation,[],[f14]) ).
fof(f17,plain,
( ( op(e0,e0) = e2
& op(e1,e1) = e2
& op(e2,e2) = e2
& op(e3,e3) = e2 )
| ~ sP1 ),
inference(nnf_transformation,[],[f13]) ).
fof(f18,plain,
( ( op(e0,e0) = e3
& op(e1,e1) = e3
& op(e2,e2) = e3
& op(e3,e3) = e3 )
| ~ sP0 ),
inference(nnf_transformation,[],[f12]) ).
fof(f19,plain,
( e0 = op(e3,e3)
| e1 = op(e3,e3)
| e2 = op(e3,e3)
| e3 = op(e3,e3) ),
inference(cnf_transformation,[],[f1]) ).
fof(f77,plain,
op(e3,e1) != op(e3,e3),
inference(cnf_transformation,[],[f4]) ).
fof(f113,plain,
op(e1,e1) != op(e3,e1),
inference(cnf_transformation,[],[f4]) ).
fof(f130,plain,
e2 = op(e3,e1),
inference(cnf_transformation,[],[f6]) ).
fof(f131,plain,
e0 = op(e1,e1),
inference(cnf_transformation,[],[f6]) ).
fof(f132,plain,
( e1 = op(e3,e3)
| ~ sP2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f133,plain,
( e1 = op(e2,e2)
| ~ sP2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f134,plain,
( e1 = op(e1,e1)
| ~ sP2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f135,plain,
( op(e0,e0) = e1
| ~ sP2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f138,plain,
( e2 = op(e1,e1)
| ~ sP1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f140,plain,
( e3 = op(e3,e3)
| ~ sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f141,plain,
( e3 = op(e2,e2)
| ~ sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f142,plain,
( e3 = op(e1,e1)
| ~ sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f143,plain,
( op(e0,e0) = e3
| ~ sP0 ),
inference(cnf_transformation,[],[f18]) ).
fof(f144,plain,
( op(e0,e0) != e3
| e3 != op(e1,e1)
| e3 != op(e2,e2)
| e3 != op(e3,e3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f146,plain,
( op(e0,e0) != e1
| e1 != op(e1,e1)
| e1 != op(e2,e2)
| e1 != op(e3,e3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f147,plain,
( e0 != op(e0,e0)
| e0 != op(e1,e1)
| e0 != op(e2,e2)
| e0 != op(e3,e3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f148,plain,
( e0 = op(e3,e3)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f149,plain,
( e0 = op(e2,e2)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f151,plain,
( e0 = op(e0,e0)
| sP2
| sP1
| sP0 ),
inference(cnf_transformation,[],[f15]) ).
fof(f153,definition,
( spl3_1
<=> e3 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f157,definition,
( spl3_2
<=> e3 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f161,definition,
( spl3_3
<=> e3 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f165,definition,
( spl3_4
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f168,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f144,f165,f161,f157,f153]) ).
fof(f170,definition,
( spl3_5
<=> e2 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f178,definition,
( spl3_7
<=> e2 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f187,definition,
( spl3_9
<=> e1 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f191,definition,
( spl3_10
<=> e1 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f195,definition,
( spl3_11
<=> e1 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f199,definition,
( spl3_12
<=> op(e0,e0) = e1 ),
introduced(definition,[new_symbols(definition,[spl3_12])],[avatar_definition]) ).
fof(f202,plain,
( ~ spl3_9
| ~ spl3_10
| ~ spl3_11
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f146,f199,f195,f191,f187]) ).
fof(f204,definition,
( spl3_13
<=> e0 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl3_13])],[avatar_definition]) ).
fof(f208,definition,
( spl3_14
<=> e0 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f212,definition,
( spl3_15
<=> e0 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl3_15])],[avatar_definition]) ).
fof(f216,definition,
( spl3_16
<=> e0 = op(e0,e0) ),
introduced(definition,[new_symbols(definition,[spl3_16])],[avatar_definition]) ).
fof(f219,plain,
( ~ spl3_13
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f147,f216,f212,f208,f204]) ).
fof(f221,definition,
( spl3_17
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl3_17])],[avatar_definition]) ).
fof(f225,definition,
( spl3_18
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl3_18])],[avatar_definition]) ).
fof(f229,definition,
( spl3_19
<=> sP2 ),
introduced(definition,[new_symbols(definition,[spl3_19])],[avatar_definition]) ).
fof(f232,plain,
( spl3_17
| spl3_18
| spl3_19
| spl3_13 ),
inference(avatar_split_clause,[],[f148,f204,f229,f225,f221]) ).
fof(f233,plain,
( spl3_17
| spl3_18
| spl3_19
| spl3_14 ),
inference(avatar_split_clause,[],[f149,f208,f229,f225,f221]) ).
fof(f235,plain,
( spl3_17
| spl3_18
| spl3_19
| spl3_16 ),
inference(avatar_split_clause,[],[f151,f216,f229,f225,f221]) ).
fof(f236,plain,
( ~ spl3_17
| spl3_1 ),
inference(avatar_split_clause,[],[f140,f153,f221]) ).
fof(f237,plain,
( ~ spl3_17
| spl3_2 ),
inference(avatar_split_clause,[],[f141,f157,f221]) ).
fof(f238,plain,
( ~ spl3_17
| spl3_3 ),
inference(avatar_split_clause,[],[f142,f161,f221]) ).
fof(f239,plain,
( ~ spl3_17
| spl3_4 ),
inference(avatar_split_clause,[],[f143,f165,f221]) ).
fof(f242,plain,
( ~ spl3_18
| spl3_7 ),
inference(avatar_split_clause,[],[f138,f178,f225]) ).
fof(f244,plain,
( ~ spl3_19
| spl3_9 ),
inference(avatar_split_clause,[],[f132,f187,f229]) ).
fof(f245,plain,
( ~ spl3_19
| spl3_10 ),
inference(avatar_split_clause,[],[f133,f191,f229]) ).
fof(f246,plain,
( ~ spl3_19
| spl3_11 ),
inference(avatar_split_clause,[],[f134,f195,f229]) ).
fof(f247,plain,
( ~ spl3_19
| spl3_12 ),
inference(avatar_split_clause,[],[f135,f199,f229]) ).
fof(f248,plain,
spl3_15,
inference(avatar_split_clause,[],[f131,f212]) ).
fof(f249,plain,
e2 != op(e3,e3),
inference(forward_demodulation,[],[f77,f130]) ).
fof(f253,plain,
e2 != op(e1,e1),
inference(forward_demodulation,[],[f113,f130]) ).
fof(f478,plain,
( spl3_1
| spl3_5
| spl3_9
| spl3_13 ),
inference(avatar_split_clause,[],[f19,f204,f187,f170,f153]) ).
fof(f493,plain,
~ spl3_5,
inference(avatar_split_clause,[],[f249,f170]) ).
fof(f497,plain,
~ spl3_7,
inference(avatar_split_clause,[],[f253,f178]) ).
cnf(s1,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f168]) ).
cnf(s3,plain,
( ~ spl3_9
| ~ spl3_10
| ~ spl3_11
| ~ spl3_12 ),
inference(sat_conversion,[],[f202]) ).
cnf(s4,plain,
( ~ spl3_13
| ~ spl3_14
| ~ spl3_15
| ~ spl3_16 ),
inference(sat_conversion,[],[f219]) ).
cnf(s5,plain,
( spl3_13
| spl3_17
| spl3_18
| spl3_19 ),
inference(sat_conversion,[],[f232]) ).
cnf(s6,plain,
( spl3_14
| spl3_17
| spl3_18
| spl3_19 ),
inference(sat_conversion,[],[f233]) ).
cnf(s8,plain,
( spl3_16
| spl3_17
| spl3_18
| spl3_19 ),
inference(sat_conversion,[],[f235]) ).
cnf(s9,plain,
( spl3_1
| ~ spl3_17 ),
inference(sat_conversion,[],[f236]) ).
cnf(s10,plain,
( spl3_2
| ~ spl3_17 ),
inference(sat_conversion,[],[f237]) ).
cnf(s11,plain,
( spl3_3
| ~ spl3_17 ),
inference(sat_conversion,[],[f238]) ).
cnf(s12,plain,
( spl3_4
| ~ spl3_17 ),
inference(sat_conversion,[],[f239]) ).
cnf(s15,plain,
( spl3_7
| ~ spl3_18 ),
inference(sat_conversion,[],[f242]) ).
cnf(s17,plain,
( spl3_9
| ~ spl3_19 ),
inference(sat_conversion,[],[f244]) ).
cnf(s18,plain,
( spl3_10
| ~ spl3_19 ),
inference(sat_conversion,[],[f245]) ).
cnf(s19,plain,
( spl3_11
| ~ spl3_19 ),
inference(sat_conversion,[],[f246]) ).
cnf(s20,plain,
( spl3_12
| ~ spl3_19 ),
inference(sat_conversion,[],[f247]) ).
cnf(s21,plain,
spl3_15,
inference(sat_conversion,[],[f248]) ).
cnf(s47,plain,
( spl3_1
| spl3_5
| spl3_9
| spl3_13 ),
inference(sat_conversion,[],[f478]) ).
cnf(s62,plain,
~ spl3_5,
inference(sat_conversion,[],[f493]) ).
cnf(s66,plain,
~ spl3_7,
inference(sat_conversion,[],[f497]) ).
cnf(s79,plain,
( spl3_1
| spl3_9
| spl3_13 ),
inference(rat,[],[s47,s62]) ).
cnf(s86,plain,
~ spl3_18,
inference(rat,[],[s15,s66]) ).
cnf(s87,plain,
( spl3_16
| spl3_17
| spl3_19 ),
inference(rat,[],[s8,s86]) ).
cnf(s88,plain,
( spl3_14
| spl3_17
| spl3_19 ),
inference(rat,[],[s6,s86]) ).
cnf(s89,plain,
( spl3_13
| spl3_17
| spl3_19 ),
inference(rat,[],[s5,s86]) ).
cnf(s90,plain,
( ~ spl3_13
| ~ spl3_14
| ~ spl3_16 ),
inference(rat,[],[s4,s21]) ).
cnf(s91,plain,
( spl3_9
| spl3_1 ),
inference(rat,[],[s90,s88,s87,s17,s79,s9]) ).
cnf(s94,plain,
( ~ spl3_19
| ~ spl3_9 ),
inference(rat,[],[s3,s18,s19,s20]) ).
cnf(s95,plain,
( spl3_19
| spl3_17 ),
inference(rat,[],[s88,s90,s87,s89]) ).
cnf(s96,plain,
spl3_1,
inference(rat,[],[s95,s94,s91,s9]) ).
cnf(s97,plain,
~ spl3_19,
inference(rat,[],[s94,s17]) ).
cnf(s98,plain,
spl3_17,
inference(rat,[],[s95,s97]) ).
cnf(s99,plain,
spl3_4,
inference(rat,[],[s12,s98]) ).
cnf(s100,plain,
spl3_3,
inference(rat,[],[s11,s98]) ).
cnf(s101,plain,
spl3_2,
inference(rat,[],[s10,s98]) ).
cnf(s102,plain,
$false,
inference(rat,[],[s1,s100,s96,s101,s99]) ).
fof(f511,plain,
$false,
inference(avatar_sat_refutation,[],[s102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG039+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 19:20:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25 % (3686754)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (3686765)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=79106747:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.25 % (3686765) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3686754-3686765"...
% 0.08/0.25 % (3686761)% WARNING: option uhcvi not known.
% 0.08/0.25 % (3686765)...printing done.
% 0.08/0.25 % (3686765)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (3686765)------------------------------
% 0.08/0.25 % (3686765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (3686765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (3686765)CaDiCaL version: 2.1.3
% 0.08/0.25 % (3686765)Termination reason: Refutation
% 0.08/0.25 % (3686765)Time elapsed: 0.004 s
% 0.08/0.25 % (3686765)Peak memory usage: 12 MB
% 0.08/0.25 % (3686765)Instructions burned: 13 (million)
% 0.08/0.25 % (3686754)Success in time 0.02 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------