%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG138+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:13:31 AM UTC 2026
% Result : Unsatisfiable 3.02s 1.10s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 38
% Syntax : Number of formulae : 226 ( 50 unt; 32 def)
% Number of atoms : 656 ( 321 equ)
% Maximal formula atoms : 128 ( 2 avg)
% Number of connectives : 711 ( 281 ~; 310 |; 88 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 33 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(f2,axiom,
( ( op(e0,e0) = e0
| op(e0,e1) = e0
| op(e0,e2) = e0
| op(e0,e3) = e0 )
& ( op(e0,e0) = e0
| op(e1,e0) = e0
| op(e2,e0) = e0
| op(e3,e0) = e0 )
& ( op(e0,e0) = e1
| op(e0,e1) = e1
| op(e0,e2) = e1
| op(e0,e3) = e1 )
& ( op(e0,e0) = e1
| op(e1,e0) = e1
| op(e2,e0) = e1
| op(e3,e0) = e1 )
& ( op(e0,e0) = e2
| op(e0,e1) = e2
| op(e0,e2) = e2
| op(e0,e3) = e2 )
& ( op(e0,e0) = e2
| op(e1,e0) = e2
| op(e2,e0) = e2
| op(e3,e0) = e2 )
& ( op(e0,e0) = e3
| op(e0,e1) = e3
| op(e0,e2) = e3
| op(e0,e3) = e3 )
& ( op(e0,e0) = e3
| op(e1,e0) = e3
| op(e2,e0) = e3
| op(e3,e0) = e3 )
& ( op(e1,e0) = e0
| op(e1,e1) = e0
| op(e1,e2) = e0
| op(e1,e3) = e0 )
& ( op(e0,e1) = e0
| op(e1,e1) = e0
| op(e2,e1) = e0
| op(e3,e1) = e0 )
& ( op(e1,e0) = e1
| op(e1,e1) = e1
| op(e1,e2) = e1
| op(e1,e3) = e1 )
& ( op(e0,e1) = e1
| op(e1,e1) = e1
| op(e2,e1) = e1
| op(e3,e1) = e1 )
& ( op(e1,e0) = e2
| op(e1,e1) = e2
| op(e1,e2) = e2
| op(e1,e3) = e2 )
& ( op(e0,e1) = e2
| op(e1,e1) = e2
| op(e2,e1) = e2
| op(e3,e1) = e2 )
& ( op(e1,e0) = e3
| op(e1,e1) = e3
| op(e1,e2) = e3
| op(e1,e3) = e3 )
& ( op(e0,e1) = e3
| op(e1,e1) = e3
| op(e2,e1) = e3
| op(e3,e1) = e3 )
& ( op(e2,e0) = e0
| op(e2,e1) = e0
| op(e2,e2) = e0
| op(e2,e3) = e0 )
& ( op(e0,e2) = e0
| op(e1,e2) = e0
| op(e2,e2) = e0
| op(e3,e2) = e0 )
& ( op(e2,e0) = e1
| op(e2,e1) = e1
| op(e2,e2) = e1
| op(e2,e3) = e1 )
& ( op(e0,e2) = e1
| op(e1,e2) = e1
| op(e2,e2) = e1
| op(e3,e2) = e1 )
& ( op(e2,e0) = e2
| op(e2,e1) = e2
| op(e2,e2) = e2
| op(e2,e3) = e2 )
& ( op(e0,e2) = e2
| op(e1,e2) = e2
| op(e2,e2) = e2
| op(e3,e2) = e2 )
& ( op(e2,e0) = e3
| op(e2,e1) = e3
| op(e2,e2) = e3
| op(e2,e3) = e3 )
& ( op(e0,e2) = e3
| op(e1,e2) = e3
| op(e2,e2) = e3
| op(e3,e2) = e3 )
& ( op(e3,e0) = e0
| op(e3,e1) = e0
| op(e3,e2) = e0
| op(e3,e3) = e0 )
& ( op(e0,e3) = e0
| op(e1,e3) = e0
| op(e2,e3) = e0
| op(e3,e3) = e0 )
& ( op(e3,e0) = e1
| op(e3,e1) = e1
| op(e3,e2) = e1
| op(e3,e3) = e1 )
& ( op(e0,e3) = e1
| op(e1,e3) = e1
| op(e2,e3) = e1
| op(e3,e3) = e1 )
& ( op(e3,e0) = e2
| op(e3,e1) = e2
| op(e3,e2) = e2
| op(e3,e3) = e2 )
& ( op(e0,e3) = e2
| op(e1,e3) = e2
| op(e2,e3) = e2
| op(e3,e3) = e2 )
& ( op(e3,e0) = e3
| op(e3,e1) = e3
| op(e3,e2) = e3
| op(e3,e3) = e3 )
& ( op(e0,e3) = e3
| op(e1,e3) = e3
| op(e2,e3) = e3
| op(e3,e3) = e3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f3,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',ax3) ).
fof(f4,axiom,
( e0 != e1
& e0 != e2
& e0 != e3
& e1 != e2
& e1 != e3
& e2 != e3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f5,axiom,
( op(e0,e0) = e0
& op(e1,e1) = e1
& op(e2,e2) = e2
& op(e3,e3) = e3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f28,axiom,
~ ( e3 = op(e0,e1)
& e2 = op(op(e0,e1),e1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f29,axiom,
~ ( e3 = op(e1,e0)
& e2 = op(op(e1,e0),e0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
fof(f52,plain,
( e3 != op(e0,e1)
| e2 != op(op(e0,e1),e1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f53,plain,
( e3 != op(e1,e0)
| e2 != op(op(e1,e0),e0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f73,plain,
( e2 = op(e3,e0)
| e2 = op(e3,e1)
| e2 = op(e3,e2)
| e2 = op(e3,e3) ),
inference(cnf_transformation,[],[f2]) ).
fof(f75,plain,
( e1 = op(e3,e0)
| e1 = op(e3,e1)
| e1 = op(e3,e2)
| e1 = op(e3,e3) ),
inference(cnf_transformation,[],[f2]) ).
fof(f77,plain,
( e0 = op(e3,e0)
| e0 = op(e3,e1)
| e0 = op(e3,e2)
| e0 = op(e3,e3) ),
inference(cnf_transformation,[],[f2]) ).
fof(f82,plain,
( e1 = op(e0,e2)
| e1 = op(e1,e2)
| e1 = op(e2,e2)
| e1 = op(e3,e2) ),
inference(cnf_transformation,[],[f2]) ).
fof(f84,plain,
( e0 = op(e0,e2)
| e0 = op(e1,e2)
| e0 = op(e2,e2)
| e0 = op(e3,e2) ),
inference(cnf_transformation,[],[f2]) ).
fof(f87,plain,
( e3 = op(e1,e0)
| e3 = op(e1,e1)
| e3 = op(e1,e2)
| e3 = op(e1,e3) ),
inference(cnf_transformation,[],[f2]) ).
fof(f95,plain,
( op(e0,e0) = e3
| e3 = op(e0,e1)
| e3 = op(e0,e2)
| e3 = op(e0,e3) ),
inference(cnf_transformation,[],[f2]) ).
fof(f116,plain,
op(e1,e1) != op(e1,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f124,plain,
op(e0,e0) != op(e0,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f127,plain,
op(e1,e3) != op(e3,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f129,plain,
op(e0,e3) != op(e3,e3),
inference(cnf_transformation,[],[f3]) ).
fof(f132,plain,
op(e2,e2) != op(e3,e2),
inference(cnf_transformation,[],[f3]) ).
fof(f139,plain,
op(e1,e1) != op(e3,e1),
inference(cnf_transformation,[],[f3]) ).
fof(f147,plain,
op(e0,e0) != op(e3,e0),
inference(cnf_transformation,[],[f3]) ).
fof(f150,plain,
e2 != e3,
inference(cnf_transformation,[],[f4]) ).
fof(f151,plain,
e1 != e3,
inference(cnf_transformation,[],[f4]) ).
fof(f152,plain,
e1 != e2,
inference(cnf_transformation,[],[f4]) ).
fof(f153,plain,
e0 != e3,
inference(cnf_transformation,[],[f4]) ).
fof(f154,plain,
e0 != e2,
inference(cnf_transformation,[],[f4]) ).
fof(f155,plain,
e0 != e1,
inference(cnf_transformation,[],[f4]) ).
fof(f156,plain,
e3 = op(e3,e3),
inference(cnf_transformation,[],[f5]) ).
fof(f157,plain,
e2 = op(e2,e2),
inference(cnf_transformation,[],[f5]) ).
fof(f158,plain,
e1 = op(e1,e1),
inference(cnf_transformation,[],[f5]) ).
fof(f159,plain,
e0 = op(e0,e0),
inference(cnf_transformation,[],[f5]) ).
fof(f182,plain,
( e3 != op(e0,e1)
| e2 != op(op(e0,e1),e1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f183,plain,
( e3 != op(e1,e0)
| e2 != op(op(e1,e0),e0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f185,definition,
( spl0_1
<=> e2 = op(op(e1,e0),e0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f187,plain,
( e2 != op(op(e1,e0),e0)
| spl0_1 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f189,definition,
( spl0_2
<=> e3 = op(e1,e0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f190,plain,
( e3 = op(e1,e0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f192,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f183,f189,f185]) ).
fof(f194,definition,
( spl0_3
<=> e2 = op(op(e0,e1),e1) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f196,plain,
( e2 != op(op(e0,e1),e1)
| spl0_3 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f198,definition,
( spl0_4
<=> e3 = op(e0,e1) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f199,plain,
( e3 = op(e0,e1)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f182,f198,f194]) ).
fof(f216,definition,
( spl0_8
<=> e3 = op(e0,e2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f217,plain,
( e3 = op(e0,e2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f234,definition,
( spl0_12
<=> e3 = op(e1,e2) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f235,plain,
( e3 = op(e1,e2)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f261,definition,
( spl0_18
<=> e2 = op(e3,e0) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f262,plain,
( e2 = op(e3,e0)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f279,definition,
( spl0_22
<=> e2 = op(e3,e1) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f280,plain,
( e2 = op(e3,e1)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f306,definition,
( spl0_28
<=> e1 = op(e0,e2) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f307,plain,
( e1 = op(e0,e2)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f315,definition,
( spl0_30
<=> e1 = op(e3,e0) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
fof(f316,plain,
( e1 = op(e3,e0)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f333,definition,
( spl0_34
<=> e1 = op(e3,e2) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f334,plain,
( e1 = op(e3,e2)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f360,definition,
( spl0_40
<=> e0 = op(e1,e2) ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f361,plain,
( e0 = op(e1,e2)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f369,definition,
( spl0_42
<=> e0 = op(e3,e1) ),
introduced(definition,[new_symbols(definition,[spl0_42])],[avatar_definition]) ).
fof(f370,plain,
( e0 = op(e3,e1)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f387,definition,
( spl0_46
<=> e0 = op(e3,e2) ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f388,plain,
( e0 = op(e3,e2)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f401,definition,
( spl0_49
<=> e3 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f403,plain,
( e3 = op(e3,e3)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f409,definition,
( spl0_51
<=> e3 = op(e1,e3) ),
introduced(definition,[new_symbols(definition,[spl0_51])],[avatar_definition]) ).
fof(f413,definition,
( spl0_52
<=> e3 = op(e0,e3) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f431,definition,
( spl0_56
<=> e2 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl0_56])],[avatar_definition]) ).
fof(f433,plain,
( e2 = op(e3,e3)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f440,definition,
( spl0_58
<=> e2 = op(e3,e2) ),
introduced(definition,[new_symbols(definition,[spl0_58])],[avatar_definition]) ).
fof(f443,plain,
( spl0_56
| spl0_58
| spl0_22
| spl0_18 ),
inference(avatar_split_clause,[],[f73,f261,f279,f440,f431]) ).
fof(f445,definition,
( spl0_59
<=> e1 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl0_59])],[avatar_definition]) ).
fof(f447,plain,
( e1 = op(e3,e3)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f454,definition,
( spl0_61
<=> e1 = op(e3,e1) ),
introduced(definition,[new_symbols(definition,[spl0_61])],[avatar_definition]) ).
fof(f457,plain,
( spl0_59
| spl0_34
| spl0_61
| spl0_30 ),
inference(avatar_split_clause,[],[f75,f315,f454,f333,f445]) ).
fof(f459,definition,
( spl0_62
<=> e0 = op(e3,e3) ),
introduced(definition,[new_symbols(definition,[spl0_62])],[avatar_definition]) ).
fof(f461,plain,
( e0 = op(e3,e3)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f459]) ).
fof(f468,definition,
( spl0_64
<=> e0 = op(e3,e0) ),
introduced(definition,[new_symbols(definition,[spl0_64])],[avatar_definition]) ).
fof(f471,plain,
( spl0_62
| spl0_46
| spl0_42
| spl0_64 ),
inference(avatar_split_clause,[],[f77,f468,f369,f387,f459]) ).
fof(f479,definition,
( spl0_66
<=> e2 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl0_66])],[avatar_definition]) ).
fof(f481,plain,
( e2 = op(e2,e2)
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f501,definition,
( spl0_71
<=> e1 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl0_71])],[avatar_definition]) ).
fof(f503,plain,
( e1 = op(e2,e2)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f505,definition,
( spl0_72
<=> e1 = op(e1,e2) ),
introduced(definition,[new_symbols(definition,[spl0_72])],[avatar_definition]) ).
fof(f508,plain,
( spl0_34
| spl0_71
| spl0_72
| spl0_28 ),
inference(avatar_split_clause,[],[f82,f306,f505,f501,f333]) ).
fof(f515,definition,
( spl0_74
<=> e0 = op(e2,e2) ),
introduced(definition,[new_symbols(definition,[spl0_74])],[avatar_definition]) ).
fof(f517,plain,
( e0 = op(e2,e2)
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f519,definition,
( spl0_75
<=> e0 = op(e0,e2) ),
introduced(definition,[new_symbols(definition,[spl0_75])],[avatar_definition]) ).
fof(f522,plain,
( spl0_46
| spl0_74
| spl0_40
| spl0_75 ),
inference(avatar_split_clause,[],[f84,f519,f360,f515,f387]) ).
fof(f529,definition,
( spl0_77
<=> e3 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl0_77])],[avatar_definition]) ).
fof(f531,plain,
( e3 = op(e1,e1)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f529]) ).
fof(f533,plain,
( spl0_51
| spl0_12
| spl0_77
| spl0_2 ),
inference(avatar_split_clause,[],[f87,f189,f529,f234,f409]) ).
fof(f541,definition,
( spl0_79
<=> e1 = op(e1,e1) ),
introduced(definition,[new_symbols(definition,[spl0_79])],[avatar_definition]) ).
fof(f543,plain,
( e1 = op(e1,e1)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f541]) ).
fof(f569,definition,
( spl0_85
<=> op(e0,e0) = e3 ),
introduced(definition,[new_symbols(definition,[spl0_85])],[avatar_definition]) ).
fof(f571,plain,
( op(e0,e0) = e3
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f573,plain,
( spl0_52
| spl0_8
| spl0_4
| spl0_85 ),
inference(avatar_split_clause,[],[f95,f569,f198,f216,f413]) ).
fof(f587,definition,
( spl0_88
<=> e0 = op(e0,e0) ),
introduced(definition,[new_symbols(definition,[spl0_88])],[avatar_definition]) ).
fof(f589,plain,
( e0 = op(e0,e0)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f608,plain,
spl0_49,
inference(avatar_split_clause,[],[f156,f401]) ).
fof(f609,plain,
spl0_66,
inference(avatar_split_clause,[],[f157,f479]) ).
fof(f610,plain,
spl0_79,
inference(avatar_split_clause,[],[f158,f541]) ).
fof(f611,plain,
spl0_88,
inference(avatar_split_clause,[],[f159,f587]) ).
fof(f624,plain,
( e1 = e3
| ~ spl0_8
| ~ spl0_28 ),
inference(forward_demodulation,[],[f217,f307]) ).
fof(f628,plain,
( $false
| ~ spl0_8
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f624,f151]) ).
fof(f629,plain,
( ~ spl0_8
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f628]) ).
fof(f633,plain,
( e0 = e3
| ~ spl0_12
| ~ spl0_40 ),
inference(forward_demodulation,[],[f235,f361]) ).
fof(f636,plain,
( $false
| ~ spl0_12
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[],[f633,f153]) ).
fof(f637,plain,
( ~ spl0_12
| ~ spl0_40 ),
inference(avatar_contradiction_clause,[],[f636]) ).
fof(f709,plain,
( e2 = e3
| ~ spl0_49
| ~ spl0_56 ),
inference(superposition,[],[f433,f403]) ).
fof(f713,plain,
( $false
| ~ spl0_49
| ~ spl0_56 ),
inference(forward_subsumption_resolution,[],[f709,f150]) ).
fof(f714,plain,
( ~ spl0_49
| ~ spl0_56 ),
inference(avatar_contradiction_clause,[],[f713]) ).
fof(f765,plain,
( e1 = e3
| ~ spl0_49
| ~ spl0_59 ),
inference(superposition,[],[f447,f403]) ).
fof(f769,plain,
( $false
| ~ spl0_49
| ~ spl0_59 ),
inference(forward_subsumption_resolution,[],[f765,f151]) ).
fof(f770,plain,
( ~ spl0_49
| ~ spl0_59 ),
inference(avatar_contradiction_clause,[],[f769]) ).
fof(f778,plain,
( e0 = e2
| ~ spl0_66
| ~ spl0_74 ),
inference(superposition,[],[f517,f481]) ).
fof(f782,plain,
( $false
| ~ spl0_66
| ~ spl0_74 ),
inference(forward_subsumption_resolution,[],[f778,f154]) ).
fof(f783,plain,
( ~ spl0_66
| ~ spl0_74 ),
inference(avatar_contradiction_clause,[],[f782]) ).
fof(f793,plain,
( e1 = e2
| ~ spl0_66
| ~ spl0_71 ),
inference(superposition,[],[f503,f481]) ).
fof(f797,plain,
( $false
| ~ spl0_66
| ~ spl0_71 ),
inference(forward_subsumption_resolution,[],[f793,f152]) ).
fof(f798,plain,
( ~ spl0_66
| ~ spl0_71 ),
inference(avatar_contradiction_clause,[],[f797]) ).
fof(f806,plain,
( e0 = e2
| ~ spl0_22
| ~ spl0_42 ),
inference(forward_demodulation,[],[f280,f370]) ).
fof(f808,plain,
( $false
| ~ spl0_22
| ~ spl0_42 ),
inference(forward_subsumption_resolution,[],[f806,f154]) ).
fof(f809,plain,
( ~ spl0_22
| ~ spl0_42 ),
inference(avatar_contradiction_clause,[],[f808]) ).
fof(f837,plain,
( e0 = e3
| ~ spl0_49
| ~ spl0_62 ),
inference(superposition,[],[f461,f403]) ).
fof(f841,plain,
( $false
| ~ spl0_49
| ~ spl0_62 ),
inference(forward_subsumption_resolution,[],[f837,f153]) ).
fof(f842,plain,
( ~ spl0_49
| ~ spl0_62 ),
inference(avatar_contradiction_clause,[],[f841]) ).
fof(f847,plain,
( e1 = e3
| ~ spl0_77
| ~ spl0_79 ),
inference(superposition,[],[f543,f531]) ).
fof(f851,plain,
( $false
| ~ spl0_77
| ~ spl0_79 ),
inference(forward_subsumption_resolution,[],[f847,f151]) ).
fof(f852,plain,
( ~ spl0_77
| ~ spl0_79 ),
inference(avatar_contradiction_clause,[],[f851]) ).
fof(f875,plain,
( e0 = e3
| ~ spl0_85
| ~ spl0_88 ),
inference(superposition,[],[f589,f571]) ).
fof(f879,plain,
( $false
| ~ spl0_85
| ~ spl0_88 ),
inference(forward_subsumption_resolution,[],[f875,f153]) ).
fof(f880,plain,
( ~ spl0_85
| ~ spl0_88 ),
inference(avatar_contradiction_clause,[],[f879]) ).
fof(f910,plain,
( e1 = e2
| ~ spl0_18
| ~ spl0_30 ),
inference(forward_demodulation,[],[f262,f316]) ).
fof(f913,plain,
( $false
| ~ spl0_18
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f910,f152]) ).
fof(f914,plain,
( ~ spl0_18
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f913]) ).
fof(f927,plain,
( e0 = e1
| ~ spl0_34
| ~ spl0_46 ),
inference(forward_demodulation,[],[f334,f388]) ).
fof(f929,plain,
( $false
| ~ spl0_34
| ~ spl0_46 ),
inference(forward_subsumption_resolution,[],[f927,f155]) ).
fof(f930,plain,
( ~ spl0_34
| ~ spl0_46 ),
inference(avatar_contradiction_clause,[],[f929]) ).
fof(f1165,plain,
( e3 != op(e1,e3)
| ~ spl0_49 ),
inference(forward_demodulation,[],[f127,f403]) ).
fof(f1169,plain,
( e3 != op(e0,e3)
| ~ spl0_49 ),
inference(forward_demodulation,[],[f129,f403]) ).
fof(f1209,plain,
( e2 != op(e3,e1)
| spl0_3
| ~ spl0_4 ),
inference(forward_demodulation,[],[f196,f199]) ).
fof(f1210,plain,
( $false
| spl0_3
| ~ spl0_4
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1209,f280]) ).
fof(f1211,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1210]) ).
fof(f1214,plain,
( ~ spl0_51
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f1165,f401,f409]) ).
fof(f1221,plain,
( e0 != op(e0,e2)
| ~ spl0_88 ),
inference(forward_demodulation,[],[f124,f589]) ).
fof(f1225,plain,
( ~ spl0_52
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f1169,f401,f413]) ).
fof(f1229,plain,
( e1 != op(e1,e2)
| ~ spl0_79 ),
inference(forward_demodulation,[],[f116,f543]) ).
fof(f1240,plain,
( ~ spl0_75
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1221,f587,f519]) ).
fof(f1243,plain,
( ~ spl0_72
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f1229,f541,f505]) ).
fof(f1246,plain,
( e2 != op(e3,e2)
| ~ spl0_66 ),
inference(forward_demodulation,[],[f132,f481]) ).
fof(f1247,plain,
( e0 != op(e3,e0)
| ~ spl0_88 ),
inference(forward_demodulation,[],[f147,f589]) ).
fof(f1249,plain,
( e1 != op(e3,e1)
| ~ spl0_79 ),
inference(forward_demodulation,[],[f139,f543]) ).
fof(f1252,plain,
( ~ spl0_58
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1246,f479,f440]) ).
fof(f1253,plain,
( ~ spl0_64
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1247,f587,f468]) ).
fof(f1254,plain,
( ~ spl0_61
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f1249,f541,f454]) ).
fof(f1336,plain,
( e2 != op(e3,e0)
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f187,f190]) ).
fof(f1337,plain,
( $false
| spl0_1
| ~ spl0_2
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1336,f262]) ).
fof(f1338,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1337]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f192]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f201]) ).
cnf(s28,plain,
( spl0_18
| spl0_22
| spl0_56
| spl0_58 ),
inference(sat_conversion,[],[f443]) ).
cnf(s30,plain,
( spl0_30
| spl0_34
| spl0_59
| spl0_61 ),
inference(sat_conversion,[],[f457]) ).
cnf(s32,plain,
( spl0_42
| spl0_46
| spl0_62
| spl0_64 ),
inference(sat_conversion,[],[f471]) ).
cnf(s37,plain,
( spl0_28
| spl0_34
| spl0_71
| spl0_72 ),
inference(sat_conversion,[],[f508]) ).
cnf(s39,plain,
( spl0_40
| spl0_46
| spl0_74
| spl0_75 ),
inference(sat_conversion,[],[f522]) ).
cnf(s42,plain,
( spl0_2
| spl0_12
| spl0_51
| spl0_77 ),
inference(sat_conversion,[],[f533]) ).
cnf(s50,plain,
( spl0_4
| spl0_8
| spl0_52
| spl0_85 ),
inference(sat_conversion,[],[f573]) ).
cnf(s73,plain,
spl0_49,
inference(sat_conversion,[],[f608]) ).
cnf(s74,plain,
spl0_66,
inference(sat_conversion,[],[f609]) ).
cnf(s75,plain,
spl0_79,
inference(sat_conversion,[],[f610]) ).
cnf(s76,plain,
spl0_88,
inference(sat_conversion,[],[f611]) ).
cnf(s80,plain,
( ~ spl0_8
| ~ spl0_28 ),
inference(sat_conversion,[],[f629]) ).
cnf(s82,plain,
( ~ spl0_12
| ~ spl0_40 ),
inference(sat_conversion,[],[f637]) ).
cnf(s101,plain,
( ~ spl0_49
| ~ spl0_56 ),
inference(sat_conversion,[],[f714]) ).
cnf(s112,plain,
( ~ spl0_49
| ~ spl0_59 ),
inference(sat_conversion,[],[f770]) ).
cnf(s114,plain,
( ~ spl0_66
| ~ spl0_74 ),
inference(sat_conversion,[],[f783]) ).
cnf(s118,plain,
( ~ spl0_66
| ~ spl0_71 ),
inference(sat_conversion,[],[f798]) ).
cnf(s121,plain,
( ~ spl0_22
| ~ spl0_42 ),
inference(sat_conversion,[],[f809]) ).
cnf(s127,plain,
( ~ spl0_49
| ~ spl0_62 ),
inference(sat_conversion,[],[f842]) ).
cnf(s129,plain,
( ~ spl0_77
| ~ spl0_79 ),
inference(sat_conversion,[],[f852]) ).
cnf(s135,plain,
( ~ spl0_85
| ~ spl0_88 ),
inference(sat_conversion,[],[f880]) ).
cnf(s143,plain,
( ~ spl0_18
| ~ spl0_30 ),
inference(sat_conversion,[],[f914]) ).
cnf(s146,plain,
( ~ spl0_34
| ~ spl0_46 ),
inference(sat_conversion,[],[f930]) ).
cnf(s175,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_22 ),
inference(sat_conversion,[],[f1211]) ).
cnf(s176,plain,
( ~ spl0_49
| ~ spl0_51 ),
inference(sat_conversion,[],[f1214]) ).
cnf(s181,plain,
( ~ spl0_49
| ~ spl0_52 ),
inference(sat_conversion,[],[f1225]) ).
cnf(s192,plain,
( ~ spl0_75
| ~ spl0_88 ),
inference(sat_conversion,[],[f1240]) ).
cnf(s195,plain,
( ~ spl0_72
| ~ spl0_79 ),
inference(sat_conversion,[],[f1243]) ).
cnf(s200,plain,
( ~ spl0_58
| ~ spl0_66 ),
inference(sat_conversion,[],[f1252]) ).
cnf(s201,plain,
( ~ spl0_64
| ~ spl0_88 ),
inference(sat_conversion,[],[f1253]) ).
cnf(s202,plain,
( ~ spl0_61
| ~ spl0_79 ),
inference(sat_conversion,[],[f1254]) ).
cnf(s204,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_18 ),
inference(sat_conversion,[],[f1338]) ).
cnf(s206,plain,
~ spl0_64,
inference(rat,[],[s201,s76]) ).
cnf(s210,plain,
~ spl0_75,
inference(rat,[],[s192,s76]) ).
cnf(s213,plain,
~ spl0_85,
inference(rat,[],[s135,s76]) ).
cnf(s214,plain,
~ spl0_61,
inference(rat,[],[s202,s75]) ).
cnf(s215,plain,
~ spl0_72,
inference(rat,[],[s195,s75]) ).
cnf(s222,plain,
~ spl0_77,
inference(rat,[],[s129,s75]) ).
cnf(s223,plain,
~ spl0_58,
inference(rat,[],[s200,s74]) ).
cnf(s229,plain,
~ spl0_71,
inference(rat,[],[s118,s74]) ).
cnf(s230,plain,
~ spl0_74,
inference(rat,[],[s114,s74]) ).
cnf(s234,plain,
~ spl0_52,
inference(rat,[],[s181,s73]) ).
cnf(s235,plain,
~ spl0_51,
inference(rat,[],[s176,s73]) ).
cnf(s236,plain,
~ spl0_62,
inference(rat,[],[s127,s73]) ).
cnf(s237,plain,
~ spl0_59,
inference(rat,[],[s112,s73]) ).
cnf(s238,plain,
~ spl0_56,
inference(rat,[],[s101,s73]) ).
cnf(s255,plain,
( spl0_4
| spl0_8 ),
inference(rat,[],[s50,s213,s234]) ).
cnf(s261,plain,
( spl0_2
| spl0_12 ),
inference(rat,[],[s42,s222,s235]) ).
cnf(s264,plain,
( spl0_40
| spl0_46 ),
inference(rat,[],[s39,s210,s230]) ).
cnf(s266,plain,
( spl0_28
| spl0_34 ),
inference(rat,[],[s37,s215,s229]) ).
cnf(s269,plain,
( spl0_42
| spl0_46 ),
inference(rat,[],[s32,s206,s236]) ).
cnf(s271,plain,
( spl0_30
| spl0_34 ),
inference(rat,[],[s30,s214,s237]) ).
cnf(s273,plain,
( spl0_18
| spl0_22 ),
inference(rat,[],[s28,s223,s238]) ).
cnf(s275,plain,
spl0_34,
inference(rat,[],[s175,s2,s273,s255,s143,s80,s271,s266]) ).
cnf(s276,plain,
~ spl0_46,
inference(rat,[],[s146,s275]) ).
cnf(s278,plain,
spl0_40,
inference(rat,[],[s264,s276]) ).
cnf(s279,plain,
spl0_42,
inference(rat,[],[s269,s276]) ).
cnf(s280,plain,
~ spl0_12,
inference(rat,[],[s82,s278]) ).
cnf(s282,plain,
~ spl0_22,
inference(rat,[],[s121,s279]) ).
cnf(s284,plain,
spl0_2,
inference(rat,[],[s261,s280]) ).
cnf(s287,plain,
spl0_18,
inference(rat,[],[s273,s282]) ).
cnf(s288,plain,
spl0_1,
inference(rat,[],[s204,s284,s287]) ).
cnf(s290,plain,
$false,
inference(rat,[],[s1,s284,s288]) ).
fof(f1339,plain,
$false,
inference(avatar_sat_refutation,[],[s290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG138+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.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 19:31:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.02/1.10 % (2093166)Detected formulas, will run a generic FOF schedule.
% 3.02/1.10 % (2093175)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=434083891:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.02/1.10 % (2093175)Refutation not found, incomplete strategy
% 3.02/1.10 % (2093175)------------------------------
% 3.02/1.10 % (2093175)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.10 % (2093175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.10 % (2093175)CaDiCaL version: 2.1.3
% 3.02/1.10 % (2093175)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.10 % (2093175)Time elapsed: 0.0000 s
% 3.02/1.10 % (2093175)Peak memory usage: 86 MB
% 3.02/1.10 % (2093171)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2396114590:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.02/1.10 % (2093176)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3679208396:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.02/1.10 % (2093177)dis-21_1_sil=8000:lcm=predicate:random_seed=1556888303:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.02/1.10 % (2093174)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1092744109:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.02/1.10 % (2093173)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2472929234:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.02/1.10 % (2093172)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3579698013:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.02/1.10 % (2093174)Refutation not found, incomplete strategy
% 3.02/1.10 % (2093174)------------------------------
% 3.02/1.10 % (2093174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.10 % (2093174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.10 % (2093174)CaDiCaL version: 2.1.3
% 3.02/1.10 % (2093174)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.10 % (2093174)Time elapsed: 0.001 s
% 3.02/1.10 % (2093174)Peak memory usage: 86 MB
% 3.02/1.10 % (2093177)Refutation not found, incomplete strategy
% 3.02/1.10 % (2093177)------------------------------
% 3.02/1.10 % (2093177)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.10 % (2093177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.10 % (2093177)CaDiCaL version: 2.1.3
% 3.02/1.10 % (2093177)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.10 % (2093177)Time elapsed: 0.007 s
% 3.02/1.10 % (2093177)Peak memory usage: 88 MB
% 3.02/1.10 % (2093177)Instructions burned: 11 (million)
% 3.02/1.10 % (2093176)First to succeed.
% 3.02/1.10 % (2093176)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2093166"
% 3.02/1.10 % (2093175)------------------------------
% 3.02/1.10 % (2093175)------------------------------
% 3.02/1.10 % (2093185)lrs+10_1_sil=8000:sp=occurrence:random_seed=427267251:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.02/1.10 % (2093185)Refutation not found, incomplete strategy
% 3.02/1.10 % (2093185)------------------------------
% 3.02/1.10 % (2093185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.02/1.10 % (2093185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.02/1.10 % (2093185)CaDiCaL version: 2.1.3
% 3.02/1.10 % (2093185)Termination reason: Refutation not found, incomplete strategy
% 3.02/1.10 % (2093185)Time elapsed: 0.0000 s
% 3.02/1.10 % (2093185)Peak memory usage: 86 MB
% 3.02/1.10 % (2093174)------------------------------
% 3.02/1.10 % (2093174)------------------------------
% 3.02/1.10 % (2093177)------------------------------
% 3.02/1.10 % (2093177)------------------------------
% 3.02/1.10 % (2093176)Refutation found. Thanks to Tanya!
% 3.02/1.10 % SZS status Unsatisfiable for theBenchmark
% 3.02/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.30 % (2093176)------------------------------
% 3.62/1.30 % (2093176)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.30 % (2093176)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.30 % (2093176)CaDiCaL version: 2.1.3
% 3.62/1.30 % (2093176)Termination reason: Refutation
% 3.62/1.30 % (2093176)Time elapsed: 0.023 s
% 3.62/1.30 % (2093176)Peak memory usage: 90 MB
% 3.62/1.30 % (2093176)Instructions burned: 41 (million)
% 3.62/1.30 % (2093176)------------------------------
% 3.62/1.30 % (2093176)------------------------------
% 3.62/1.30 % (2093166)Success in time 0.431 s
% 3.62/1.30 % Vampire exiting
%------------------------------------------------------------------------------